@article {Ham79, AUTHOR = {Hamana, Masamichi}, TITLE = {Injective envelopes of {$C\sp{\ast} $}-algebras}, JOURNAL = {J. Math. Soc. Japan}, FJOURNAL = {Journal of the Mathematical Society of Japan}, VOLUME = {31}, YEAR = {1979}, NUMBER = {1}, PAGES = {181--197}, ISSN = {0025-5645,1881-1167}, MRCLASS = {46L05}, MRNUMBER = {519044}, MRREVIEWER = {Richard\ I.\ Loebl}, DOI = {10.2969/jmsj/03110181}, URL = {https://doi.org/10.2969/jmsj/03110181}, } @misc{AHO23, title={On the amenable subalgebras of group von Neumann algebras}, author={Tattwamasi Amrutam and Yair Hartman and Hanna Oppelmayer}, year={2023}, eprint={2309.10494}, archivePrefix={arXiv}, primaryClass={math.OA} } @article {Ch74, AUTHOR = {Choi, Man Duen}, TITLE = {A {S}chwarz inequality for positive linear maps on {$C\sp{\ast} \ $}-algebras}, JOURNAL = {Illinois J. Math.}, FJOURNAL = {Illinois Journal of Mathematics}, VOLUME = {18}, YEAR = {1974}, PAGES = {565--574}, ISSN = {0019-2082}, MRCLASS = {46L05}, MRNUMBER = {355615}, MRREVIEWER = {J.\ W.\ Bunce}, URL = {http://projecteuclid.org/euclid.ijm/1256051007}, } @article{HW98, ISSN = {00029327, 10806377}, URL = {http://www.jstor.org/stable/25098610}, author = {Uffe Haagerup and Carl Winsløw}, journal = {American Journal of Mathematics}, number = {3}, pages = {567--617}, publisher = {Johns Hopkins University Press}, title = {{The Effros-Maréchal Topology in the Space of Von Neumann Algebras}}, urldate = {2024-06-05}, volume = {120}, year = {1998} } @article {BDLW16, AUTHOR = {Bader, Uri and Duchesne, Bruno and L\'{e}cureux, Jean}, TITLE = {Amenable invariant random subgroups}, NOTE = {With an appendix by Phillip Wesolek}, JOURNAL = {Israel J. Math.}, FJOURNAL = {Israel Journal of Mathematics}, VOLUME = {213}, YEAR = {2016}, NUMBER = {1}, PAGES = {399--422}, ISSN = {0021-2172,1565-8511}, MRCLASS = {22D05 (22D10 43A07)}, MRNUMBER = {3509477}, MRREVIEWER = {George\ A.\ Willis}, DOI = {10.1007/s11856-016-1324-7}, URL = {https://doi.org/10.1007/s11856-016-1324-7}, } @article {AIM21, AUTHOR = {Arano, Yuki and Isono, Yusuke and Marrakchi, Amine}, TITLE = {Ergodic theory of affine isometric actions on {H}ilbert spaces}, JOURNAL = {Geom. Funct. Anal.}, FJOURNAL = {Geometric and Functional Analysis}, VOLUME = {31}, YEAR = {2021}, NUMBER = {5}, PAGES = {1013--1094}, ISSN = {1016-443X,1420-8970}, MRCLASS = {37A40 (20E08 20F65 28C20 37A50)}, MRNUMBER = {4356699}, MRREVIEWER = {Eusebio\ Gardella}, DOI = {10.1007/s00039-021-00584-2}, URL = {https://doi.org/10.1007/s00039-021-00584-2}, } @article{AP17, title={{An introduction to $\mathrm{II}_1$ factors}}, author={Anantharaman, Claire and Popa, Sorin}, journal={preprint}, volume={8}, year={2017} } @article{BF11, ISSN = {03794024, 18417744}, URL = {http://www.jstor.org/stable/24715977}, author = {Jon P. Bannon and Junsheng Fang}, journal = {Journal of Operator Theory}, number = {2}, pages = {403--417}, publisher = {Theta Foundation}, title = {SOME REMARKS ON {H}AAGERUP'S APPROXIMATION PROPERTY}, urldate = {2024-01-07}, volume = {65}, year = {2011} } @article {BHT14, AUTHOR = {Bowen, Lewis and Hartman, Yair and Tamuz, Omer}, TITLE = {Property ({T}) and the {F}urstenberg entropy of nonsingular actions}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {144}, YEAR = {2016}, NUMBER = {1}, PAGES = {31--39}, ISSN = {0002-9939,1088-6826}, MRCLASS = {22D10 (20F69 22F10 37A35 37A40)}, MRNUMBER = {3415574}, MRREVIEWER = {Alain\ Valette}, DOI = {10.1090/proc/12685}, URL = {https://doi.org/10.1090/proc/12685}, } @phdthesis{Bo14, title={Several rigidity features of von Neumann algebras}, author={Boutonnet, R{\'e}mi}, year={2014}, school={Ecole normale sup{\'e}rieure de lyon-ENS LYON}, URL={https://theses.hal.science/tel-01124349}, } @article {Ch83, AUTHOR = {Choda, Marie}, TITLE = {Group factors of the {H}aagerup type}, JOURNAL = {Proc. Japan Acad. Ser. A Math. Sci.}, FJOURNAL = {Japan Academy. Proceedings. Series A. Mathematical Sciences}, VOLUME = {59}, YEAR = {1983}, NUMBER = {5}, PAGES = {174--177}, ISSN = {0386-2194}, MRCLASS = {46L35}, MRNUMBER = {718798}, MRREVIEWER = {Vaughan\ Jones}, URL = {http://projecteuclid.org/euclid.pja/1195515589}, } @article {Co80, AUTHOR = {Connes, A.}, TITLE = {On the spatial theory of von {N}eumann algebras}, JOURNAL = {J. Functional Analysis}, FJOURNAL = {Journal of Functional Analysis}, VOLUME = {35}, YEAR = {1980}, NUMBER = {2}, PAGES = {153--164}, ISSN = {0022-1236}, MRCLASS = {46L10 (46L40)}, MRNUMBER = {561983}, MRREVIEWER = {Richard\ I.\ Loebl}, DOI = {10.1016/0022-1236(80)90002-6}, URL = {https://doi.org/10.1016/0022-1236(80)90002-6}, } @article {CJ85, AUTHOR = {Connes, A. and Jones, V.}, TITLE = {Property {$T$} for von {N}eumann algebras}, JOURNAL = {Bull. London Math. Soc.}, FJOURNAL = {The Bulletin of the London Mathematical Society}, VOLUME = {17}, YEAR = {1985}, NUMBER = {1}, PAGES = {57--62}, ISSN = {0024-6093,1469-2120}, MRCLASS = {46L35 (22D25)}, MRNUMBER = {766450}, MRREVIEWER = {Colin\ E.\ Sutherland}, DOI = {10.1112/blms/17.1.57}, URL = {https://doi.org/10.1112/blms/17.1.57}, } @article {DP20, AUTHOR = {Das, Sayan and Peterson, Jesse}, TITLE = {Poisson boundaries of {${\rm II}_1$} factors}, JOURNAL = {Compos. Math.}, FJOURNAL = {Compositio Mathematica}, VOLUME = {158}, YEAR = {2022}, NUMBER = {8}, PAGES = {1746--1776}, ISSN = {0010-437X,1570-5846}, MRCLASS = {46L10 (46L55)}, MRNUMBER = {4493239}, MRREVIEWER = {Jorge\ Castillejos}, DOI = {10.1112/S0010437X22007539}, URL = {https://doi.org/10.1112/S0010437X22007539}, } @article {DKP22, AUTHOR = {Ding, Changying and Elayavalli, Srivatsav Kunnawalkam and Peterson, Jesse}, TITLE = {Properly proximal von {N}eumann algebras}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {172}, YEAR = {2023}, NUMBER = {15}, PAGES = {2821--2894}, ISSN = {0012-7094,1547-7398}, MRCLASS = {99-06}, MRNUMBER = {4675043}, DOI = {10.1215/00127094-2022-0098}, URL = {https://doi.org/10.1215/00127094-2022-0098}, } @article {Fu63, AUTHOR = {Furstenberg, Harry}, TITLE = {Noncommuting random products}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {108}, YEAR = {1963}, PAGES = {377--428}, ISSN = {0002-9947,1088-6850}, MRCLASS = {60.08 (60.66)}, MRNUMBER = {163345}, MRREVIEWER = {G.-C.\ Rota}, DOI = {10.2307/1993589}, URL = {https://doi.org/10.2307/1993589}, } @article {Ha75, AUTHOR = {Haagerup, Uffe}, TITLE = {The standard form of von {N}eumann algebras}, JOURNAL = {Math. Scand.}, FJOURNAL = {Mathematica Scandinavica}, VOLUME = {37}, YEAR = {1975}, NUMBER = {2}, PAGES = {271--283}, ISSN = {0025-5521,1903-1807}, MRCLASS = {46L10}, MRNUMBER = {407615}, MRREVIEWER = {H.\ Araki}, DOI = {10.7146/math.scand.a-11606}, URL = {https://doi.org/10.7146/math.scand.a-11606}, } @article {Ha79, AUTHOR = {Haagerup, Uffe}, TITLE = {An example of a nonnuclear {$C\sp{\ast} $}-algebra, which has the metric approximation property}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {50}, YEAR = {1978/79}, NUMBER = {3}, PAGES = {279--293}, ISSN = {0020-9910,1432-1297}, MRCLASS = {46L05 (22D35 43A35)}, MRNUMBER = {520930}, MRREVIEWER = {Ole\ A.\ Nielsen}, DOI = {10.1007/BF01410082}, URL = {https://doi.org/10.1007/BF01410082}, } @article {Jo83, AUTHOR = {Jones, V. F. R.}, TITLE = {Index for subfactors}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {72}, YEAR = {1983}, NUMBER = {1}, PAGES = {1--25}, ISSN = {0020-9910,1432-1297}, MRCLASS = {46L35 (10D07)}, MRNUMBER = {696688}, MRREVIEWER = {Yasuo\ Watatani}, DOI = {10.1007/BF01389127}, URL = {https://doi.org/10.1007/BF01389127}, } @book{KR86, title={Fundamentals of the theory of operator algebras. Volume II: Advanced theory}, author={Kadison, Richard V and Ringrose, John R}, year={1986}, publisher={Academic press New York} } @article {Ka67, AUTHOR = {Ka\v{z}hdan, D. A.}, TITLE = {On the connection of the dual space of a group with the structure of its closed subgroups}, JOURNAL = {Funct. Anal. Appl.}, FJOURNAL = {Functional Analysis and Its Applications}, VOLUME = {1}, YEAR = {1967}, PAGES = {71--74}, ISSN = {0374-1990}, MRCLASS = {22.20}, MRNUMBER = {209390}, MRREVIEWER = {K.\ Strambach}, DOI = {10.1007/BF01075866}, } @article {Ne03, AUTHOR = {Nevo, Amos}, TITLE = {The spectral theory of amenable actions and invariants of discrete groups}, JOURNAL = {Geom. Dedicata}, FJOURNAL = {Geometriae Dedicata}, VOLUME = {100}, YEAR = {2003}, PAGES = {187--218}, ISSN = {0046-5755,1572-9168}, MRCLASS = {22E40 (22D40 37A15)}, MRNUMBER = {2011122}, MRREVIEWER = {Bachir\ Bekka}, DOI = {10.1023/A:1025839828396}, URL = {https://doi.org/10.1023/A:1025839828396}, } @article {OOT17, AUTHOR = {Okayasu, Rui and Ozawa, Narutaka and Tomatsu, Reiji}, TITLE = {Haagerup approximation property via bimodules}, JOURNAL = {Math. Scand.}, FJOURNAL = {Mathematica Scandinavica}, VOLUME = {121}, YEAR = {2017}, NUMBER = {1}, PAGES = {75--91}, ISSN = {0025-5521,1903-1807}, MRCLASS = {22D25 (46L52)}, MRNUMBER = {3708965}, MRREVIEWER = {Sergey\ V.\ Ludkowski}, DOI = {10.7146/math.scand.a-25970}, URL = {https://doi.org/10.7146/math.scand.a-25970}, } @article {PS12, AUTHOR = {Peterson, Jesse and Sinclair, Thomas}, TITLE = {On cocycle superrigidity for {G}aussian actions}, JOURNAL = {Ergodic Theory Dynam. Systems}, FJOURNAL = {Ergodic Theory and Dynamical Systems}, VOLUME = {32}, YEAR = {2012}, NUMBER = {1}, PAGES = {249--272}, ISSN = {0143-3857,1469-4417}, MRCLASS = {37A20 (22F10 37A15)}, MRNUMBER = {2873170}, MRREVIEWER = {Alain\ Valette}, DOI = {10.1017/S0143385710000751}, URL = {https://doi.org/10.1017/S0143385710000751}, } @article {Sh99, AUTHOR = {Shlyakhtenko, Dimitri}, TITLE = {{$A$}-valued semicircular systems}, JOURNAL = {J. Funct. Anal.}, FJOURNAL = {Journal of Functional Analysis}, VOLUME = {166}, YEAR = {1999}, NUMBER = {1}, PAGES = {1--47}, ISSN = {0022-1236,1096-0783}, MRCLASS = {46L54 (46L10 46L35)}, MRNUMBER = {1704661}, MRREVIEWER = {Ken\ Dykema}, DOI = {10.1006/jfan.1999.3424}, URL = {https://doi.org/10.1006/jfan.1999.3424}, } @article {Ta23, AUTHOR = {Tan, Hui}, TITLE = {Spectral gap characterizations of property ({T}) for {${\rm II}_1$} factors}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2023}, volume = {2023}, NUMBER = {19}, PAGES = {16994--17020}, ISSN = {1073-7928,1687-0247}, MRCLASS = {46L10 (46L55)}, MRNUMBER = {4651905}, DOI = {10.1093/imrn/rnad109}, URL = {https://doi.org/10.1093/imrn/rnad109}, } @article{Zh23, author = {Zhou, Shuoxing}, title = "{Noncommutative Poisson Boundaries, Ultraproducts, and Entropy}", JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, volume = {2024}, number = {10}, pages = {8794-8818}, year = {2024}, issn = {1073-7928}, doi = {10.1093/imrn/rnae022}, url = {https://doi.org/10.1093/imrn/rnae022}, } @article {Lo34, AUTHOR = {L\"{o}wner, Karl}, TITLE = {\"{U}ber monotone {M}atrixfunktionen}, JOURNAL = {Math. Z.}, FJOURNAL = {Mathematische Zeitschrift}, VOLUME = {38}, YEAR = {1934}, NUMBER = {1}, PAGES = {177--216}, ISSN = {0025-5874,1432-1823}, MRCLASS = {99-04}, MRNUMBER = {1545446}, DOI = {10.1007/BF01170633}, URL = {https://doi.org/10.1007/BF01170633}, } @article {He51, AUTHOR = {Heinz, Erhard}, TITLE = {Beitr\"{a}ge zur {S}t\"{o}rungstheorie der {S}pektralzerlegung}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {123}, YEAR = {1951}, PAGES = {415--438}, ISSN = {0025-5831,1432-1807}, MRCLASS = {46.3X}, MRNUMBER = {44747}, MRREVIEWER = {F.\ H.\ Brownell}, DOI = {10.1007/BF02054965}, URL = {https://doi.org/10.1007/BF02054965}, } @book {Bh97, AUTHOR = {Bhatia, Rajendra}, TITLE = {Matrix analysis}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {169}, PUBLISHER = {Springer-Verlag, New York}, YEAR = {1997}, PAGES = {xii+347}, ISBN = {0-387-94846-5}, MRCLASS = {15-02 (47-02)}, MRNUMBER = {1477662}, MRREVIEWER = {R.\ J.\ Bumcrot}, DOI = {10.1007/978-1-4612-0653-8}, URL = {https://doi.org/10.1007/978-1-4612-0653-8}, } @book {TakII, AUTHOR = {Takesaki, M.}, TITLE = {Theory of operator algebras. {II}}, SERIES = {Encyclopaedia of Mathematical Sciences}, VOLUME = {125}, NOTE = {Operator Algebras and Non-commutative Geometry, 6}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {2003}, PAGES = {xxii+518}, ISBN = {3-540-42914-X}, MRCLASS = {46L10 (47L35 47L55)}, MRNUMBER = {1943006}, MRREVIEWER = {Robert\ S.\ Doran}, DOI = {10.1007/978-3-662-10451-4}, URL = {https://doi.org/10.1007/978-3-662-10451-4}, } @article {Izu02, AUTHOR = {Izumi, Masaki}, TITLE = {Non-commutative {P}oisson boundaries and compact quantum group actions}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {169}, YEAR = {2002}, NUMBER = {1}, PAGES = {1--57}, ISSN = {0001-8708,1090-2082}, MRCLASS = {46L55 (22D25 46L65 81R50 81S25)}, MRNUMBER = {1916370}, MRREVIEWER = {Shuzhou\ Wang}, DOI = {10.1006/aima.2001.2053}, URL = {https://doi.org/10.1006/aima.2001.2053}, } @article {Fu63a, AUTHOR = {Furstenberg, Harry}, TITLE = {A {P}oisson formula for semi-simple {L}ie groups}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {77}, YEAR = {1963}, PAGES = {335--386}, ISSN = {0003-486X}, MRCLASS = {22.65}, MRNUMBER = {146298}, MRREVIEWER = {S.\ Helgason}, DOI = {10.2307/1970220}, URL = {https://doi.org/10.2307/1970220}, } @article {Zh23b, AUTHOR = {Zhou, Shuoxing}, TITLE = {Hypertrace and entropy gap characterizations of property ({T}) for {$\rm II_1$} factors}, JOURNAL = {J. Funct. Anal.}, FJOURNAL = {Journal of Functional Analysis}, VOLUME = {287}, YEAR = {2024}, NUMBER = {6}, PAGES = {Paper No. 110530}, ISSN = {0022-1236,1096-0783}, MRCLASS = {46L10 (37A55)}, MRNUMBER = {4755484}, DOI = {10.1016/j.jfa.2024.110530}, URL = {https://doi.org/10.1016/j.jfa.2024.110530}, } @book {KL16, AUTHOR = {Kerr, David and Li, Hanfeng}, TITLE = {Ergodic theory}, SERIES = {Springer Monographs in Mathematics}, NOTE = {Independence and dichotomies}, PUBLISHER = {Springer, Cham}, YEAR = {2016}, PAGES = {xxxiv+431}, ISBN = {978-3-319-49845-4; 978-3-319-49847-8}, MRCLASS = {37-02 (03E15 05D10 05D40 37Axx 37B05 37B40)}, MRNUMBER = {3616077}, MRREVIEWER = {M.\ L.\ Blank}, DOI = {10.1007/978-3-319-49847-8}, URL = {https://doi.org/10.1007/978-3-319-49847-8}, } @book {Mar91, AUTHOR = {Margulis, G. A.}, TITLE = {Discrete subgroups of semisimple {L}ie groups}, SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]}, VOLUME = {17}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {1991}, PAGES = {x+388}, ISBN = {3-540-12179-X}, MRCLASS = {22E40 (20Hxx 22-02 22D40)}, MRNUMBER = {1090825}, MRREVIEWER = {Gopal\ Prasad}, DOI = {10.1007/978-3-642-51445-6}, URL = {https://doi.org/10.1007/978-3-642-51445-6}, } @article {HK23, AUTHOR = {Hartman, Yair and Kalantar, Mehrdad}, TITLE = {Stationary {$C^*$}-dynamical systems}, NOTE = {With an appendix by Uri Bader, Hartman and Kalantar}, JOURNAL = {J. Eur. Math. Soc. (JEMS)}, FJOURNAL = {Journal of the European Mathematical Society (JEMS)}, VOLUME = {25}, YEAR = {2023}, NUMBER = {5}, PAGES = {1783--1821}, ISSN = {1435-9855,1435-9863}, MRCLASS = {46L05 (20C07 37A55 46L35 46L55)}, MRNUMBER = {4592860}, MRREVIEWER = {Catalin\ Badea}, DOI = {10.4171/jems/1225}, URL = {https://doi.org/10.4171/jems/1225}, } @article {AHW16, AUTHOR = {Ando, Hiroshi and Haagerup, Uffe and Winsl{\o}w, Carl}, TITLE = {Ultraproducts, {QWEP} von {N}eumann algebras, and the {E}ffros-{M}ar\'echal topology}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, VOLUME = {715}, YEAR = {2016}, PAGES = {231--250}, ISSN = {0075-4102,1435-5345}, MRCLASS = {46M07 (46L10 47L15)}, MRNUMBER = {3507925}, MRREVIEWER = {Ioannis\ Zarakas}, DOI = {10.1515/crelle-2014-0005}, URL = {https://doi.org/10.1515/crelle-2014-0005}, } @book {Aze70, AUTHOR = {Azencott, Robert}, TITLE = {Espaces de {P}oisson des groupes localement compacts}, SERIES = {Lecture Notes in Mathematics}, VOLUME = {Vol. 148}, PUBLISHER = {Springer-Verlag, Berlin-New York}, YEAR = {1970}, PAGES = {ix+141}, MRCLASS = {60J50 (22D40 60B15)}, MRNUMBER = {501376}, MRREVIEWER = {G.\ van\ Dijk}, } @incollection {Fur73, AUTHOR = {Furstenberg, Harry}, TITLE = {Boundary theory and stochastic processes on homogeneous spaces}, BOOKTITLE = {Harmonic analysis on homogeneous spaces ({P}roc. {S}ympos. {P}ure {M}ath., {V}ol. {XXVI}, {W}illiams {C}oll., {W}illiamstown, {M}ass., 1972)}, SERIES = {Proc. Sympos. Pure Math.}, VOLUME = {Vol. XXVI}, PAGES = {193--229}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {1973}, MRCLASS = {22E40 (60J50)}, MRNUMBER = {352328}, MRREVIEWER = {R.\ G.\ Laha}, } @article {Fur03, AUTHOR = {Furman, Alex}, TITLE = {On minimal strongly proximal actions of locally compact groups}, JOURNAL = {Israel J. Math.}, FJOURNAL = {Israel Journal of Mathematics}, VOLUME = {136}, YEAR = {2003}, PAGES = {173--187}, ISSN = {0021-2172,1565-8511}, MRCLASS = {37B05 (22D05 57S15)}, MRNUMBER = {1998109}, MRREVIEWER = {Bachir\ Bekka}, DOI = {10.1007/BF02807197}, URL = {https://doi.org/10.1007/BF02807197}, } @article{LM24, title={On dense orbits in the space of subequivalence relations}, author={Le Ma{\^\i}tre, Fran{\c{c}}ois}, journal={arXiv preprint arXiv:2405.01806}, year={2024} } @article{Kec17, title={The spaces of measure preserving equivalence relations and graphs}, author={Kechris, Alexander S}, journal={preprint}, year={2024}, URL = {https://pma.caltech.edu/documents/6021/space_of_equivalence_relations_012book.pdf}} @article{AFH24, title={Co-spectral radius for countable equivalence relations}, DOI={10.1017/etds.2024.32}, journal={Ergodic Theory and Dynamical Systems}, author={Abert, Mikl{\'o}s and Fraczyk, Mikolaj and Hayes, Benjamin}, year={2024}, pages={1–43}} @article{BCDK2024, title={Factoriality of groupoid von Neumann algebras}, author={Berendschot, Tey and Chakraborty, Soham and Donvil, Milan and Kim, Se-Jin}, journal={arXiv preprint arXiv:2402.04449}, year={2024} } @article {HK24, AUTHOR = {Hartman, Yair and Kalantar, Mehrdad}, TITLE = {Tight inclusions of {$C^*$}-dynamical systems}, JOURNAL = {Groups Geom. Dyn.}, FJOURNAL = {Groups, Geometry, and Dynamics}, VOLUME = {18}, YEAR = {2024}, NUMBER = {1}, PAGES = {67--90}, ISSN = {1661-7207,1661-7215}, MRCLASS = {37A55 (37A40 46L55 47C15)}, MRNUMBER = {4705627}, MRREVIEWER = {Francesco\ Fidaleo}, DOI = {10.4171/ggd/739}, URL = {https://doi.org/10.4171/ggd/739}, } @article {FM77, AUTHOR = {Feldman, Jacob and Moore, Calvin C.}, TITLE = {Ergodic equivalence relations, cohomology, and von {N}eumann algebras. {II}}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {234}, YEAR = {1977}, NUMBER = {2}, PAGES = {325--359}, ISSN = {0002-9947,1088-6850}, MRCLASS = {22D40 (28A65 46L10)}, MRNUMBER = {578730}, DOI = {10.2307/1997925}, URL = {https://doi.org/10.2307/1997925}, } @article {Aoi03, AUTHOR = {Aoi, Hisashi}, TITLE = {A construction of equivalence subrelations for intermediate subalgebras}, JOURNAL = {J. Math. Soc. Japan}, FJOURNAL = {Journal of the Mathematical Society of Japan}, VOLUME = {55}, YEAR = {2003}, NUMBER = {3}, PAGES = {713--725}, ISSN = {0025-5645,1881-1167}, MRCLASS = {46L10 (37A20)}, MRNUMBER = {1978219}, MRREVIEWER = {Baruch\ Solel}, DOI = {10.2969/jmsj/1191418999}, URL = {https://doi.org/10.2969/jmsj/1191418999}, } @incollection {Izu04, AUTHOR = {Izumi, Masaki}, TITLE = {Non-commutative {P}oisson boundaries}, BOOKTITLE = {Discrete geometric analysis}, SERIES = {Contemp. Math.}, VOLUME = {347}, PAGES = {69--81}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2004}, ISBN = {0-8218-3351-0}, MRCLASS = {46L53 (46L07 60J50)}, MRNUMBER = {2077031}, MRREVIEWER = {Sergey\ Neshveyev}, DOI = {10.1090/conm/347/06267}, URL = {https://doi.org/10.1090/conm/347/06267}, } @article {Pet86, AUTHOR = {Petz, D.}, TITLE = {Properties of the relative entropy of states of von {N}eumann algebras}, JOURNAL = {Acta Math. Hungar.}, FJOURNAL = {Acta Mathematica Hungarica}, VOLUME = {47}, YEAR = {1986}, NUMBER = {1-2}, PAGES = {65--72}, ISSN = {0236-5294,1588-2632}, MRCLASS = {46L50 (46L30)}, MRNUMBER = {836395}, MRREVIEWER = {Fumio\ Hiai}, DOI = {10.1007/BF01949125}, URL = {https://doi.org/10.1007/BF01949125}, } @article {NZ00, AUTHOR = {Nevo, Amos and Zimmer, Robert J.}, TITLE = {Rigidity of {F}urstenberg entropy for semisimple {L}ie group actions}, JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)}, FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. Quatri\`eme S\'erie}, VOLUME = {33}, YEAR = {2000}, NUMBER = {3}, PAGES = {321--343}, ISSN = {0012-9593}, MRCLASS = {22D40 (22E46 22F10 37A35)}, MRNUMBER = {1775184}, MRREVIEWER = {Douglas\ P.\ Dokken}, DOI = {10.1016/S0012-9593(00)00113-0}, URL = {https://doi.org/10.1016/S0012-9593(00)00113-0}, } @incollection {Fur02, AUTHOR = {Furman, Alex}, TITLE = {Random walks on groups and random transformations}, BOOKTITLE = {Handbook of dynamical systems, {V}ol.\ 1{A}}, PAGES = {931--1014}, PUBLISHER = {North-Holland, Amsterdam}, YEAR = {2002}, ISBN = {0-444-82669-6}, MRCLASS = {60G50 (37A50 37H15)}, MRNUMBER = {1928529}, MRREVIEWER = {Gernot\ Greschonig}, DOI = {10.1016/S1874-575X(02)80014-5}, URL = {https://doi.org/10.1016/S1874-575X(02)80014-5}, } @article {KV83, AUTHOR = {Ka\u{\i}manovich, V. A. and Vershik, A. M.}, TITLE = {Random walks on discrete groups: boundary and entropy}, JOURNAL = {Ann. Probab.}, FJOURNAL = {The Annals of Probability}, VOLUME = {11}, YEAR = {1983}, NUMBER = {3}, PAGES = {457--490}, ISSN = {0091-1798,2168-894X}, MRCLASS = {60B15 (43A07 60J15)}, MRNUMBER = {704539}, MRREVIEWER = {Yves\ Derriennic}, URL ={https://www.jstor.org/stable/2243645}, } @incollection {FG10, AUTHOR = {Furstenberg, Hillel and Glasner, Eli}, TITLE = {Stationary dynamical systems}, BOOKTITLE = {Dynamical numbers---interplay between dynamical systems and number theory}, SERIES = {Contemp. Math.}, VOLUME = {532}, PAGES = {1--28}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2010}, ISBN = {978-0-8218-4958-3}, MRCLASS = {22D40 (28D05 37A15 37A30 37A40 37A50)}, MRNUMBER = {2762131}, MRREVIEWER = {Thomas\ Ward}, DOI = {10.1090/conm/532/10481}, URL = {https://doi.org/10.1090/conm/532/10481}, } @misc{Zh24, title={Noncommutative topological boundaries and amenable invariant random intermediate subalgebras}, author={Shuoxing Zhou}, year={2024}, eprint={2407.10905}, archivePrefix={arXiv}, primaryClass={math.OA}, url={https://arxiv.org/abs/2407.10905}, } @article {NS13, AUTHOR = {Nevo, Amos and Sageev, Michah}, TITLE = {The {P}oisson boundary of {${\rm CAT}(0)$} cube complex groups}, JOURNAL = {Groups Geom. Dyn.}, FJOURNAL = {Groups, Geometry, and Dynamics}, VOLUME = {7}, YEAR = {2013}, NUMBER = {3}, PAGES = {653--695}, ISSN = {1661-7207,1661-7215}, MRCLASS = {20P05 (22F10 37B05 57S30 60J50)}, MRNUMBER = {3095714}, MRREVIEWER = {Alain\ Valette}, DOI = {10.4171/GGD/202}, URL = {https://doi.org/10.4171/GGD/202}, } @misc{Hou24, title={Operator algebraic characterization of the noncommutative Poisson boundary}, author={Cyril Houdayer}, year={2024}, eprint={2410.11707}, archivePrefix={arXiv}, primaryClass={math.OA}, url={https://arxiv.org/abs/2410.11707}, } @book {Gla03, AUTHOR = {Glasner, Eli}, TITLE = {Ergodic theory via joinings}, SERIES = {Mathematical Surveys and Monographs}, VOLUME = {101}, PUBLISHER = {American Mathematical Society, Providence, RI}, YEAR = {2003}, PAGES = {xii+384}, ISBN = {0-8218-3372-3}, MRCLASS = {37A15 (28Dxx 37A25 37A35 37A45 37B99 54H20)}, MRNUMBER = {1958753}, MRREVIEWER = {Andr\'es\ del\ Junco}, DOI = {10.1090/surv/101}, URL = {https://doi.org/10.1090/surv/101}, } @book {TakI, AUTHOR = {Takesaki, M.}, TITLE = {Theory of operator algebras. {I}}, SERIES = {Encyclopaedia of Mathematical Sciences}, VOLUME = {124}, NOTE = {Reprint of the first (1979) edition, Operator Algebras and Non-commutative Geometry, 5}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {2002}, PAGES = {xx+415}, ISBN = {3-540-42248-X}, MRCLASS = {46Lxx (46-01)}, MRNUMBER = {1873025}, } @misc{Iso25, title={Weak relative Dixmier property and Popa's intertwining technique for type III subfactors}, author={Yusuke Isono}, year={2025}, eprint={2508.17592}, archivePrefix={arXiv}, primaryClass={math.OA}, url={https://arxiv.org/abs/2508.17592}, } @article {Mar19, AUTHOR = {Marrakchi, Amine}, TITLE = {On the weak relative {D}ixmier property}, JOURNAL = {Proc. Lond. Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {122}, YEAR = {2021}, NUMBER = {1}, PAGES = {118--123}, ISSN = {0024-6115,1460-244X}, MRCLASS = {46L10 (46L36 46L40 46L55)}, MRNUMBER = {4210259}, MRREVIEWER = {Antonio\ M.\ Peralta}, DOI = {10.1112/plms.12347}, URL = {https://doi-org.proxy.rubens.ens.fr/10.1112/plms.12347}, } @article {Pop99, AUTHOR = {Popa, Sorin}, TITLE = {On the relative {D}ixmier property for inclusions of {$C^*$}-algebras}, JOURNAL = {J. Funct. Anal.}, FJOURNAL = {Journal of Functional Analysis}, VOLUME = {171}, YEAR = {2000}, NUMBER = {1}, PAGES = {139--154}, ISSN = {0022-1236,1096-0783}, MRCLASS = {46L37 (46L05)}, MRNUMBER = {1742862}, MRREVIEWER = {H.\ Halpern}, DOI = {10.1006/jfan.1999.3536}, URL = {https://doi-org.proxy.rubens.ens.fr/10.1006/jfan.1999.3536}, } @article {KNR14, AUTHOR = {Kalantar, Mehrdad and Neufang, Matthias and Ruan, Zhong-Jin}, TITLE = {Realization of quantum group {P}oisson boundaries as crossed products}, JOURNAL = {Bull. Lond. Math. Soc.}, FJOURNAL = {Bulletin of the London Mathematical Society}, VOLUME = {46}, YEAR = {2014}, NUMBER = {6}, PAGES = {1267--1275}, ISSN = {0024-6093,1469-2120}, MRCLASS = {46L55 (60J50)}, MRNUMBER = {3291263}, MRREVIEWER = {Rolf\ Gohm}, DOI = {10.1112/blms/bdu081}, URL = {https://doi-org.proxy.rubens.ens.fr/10.1112/blms/bdu081}, } @article{Connes1976Injective, author = {Connes, Alain}, title = {Classification of injective factors. Cases {$\mathrm{II}_1$}, {$\mathrm{II}_\infty$}, {$\mathrm{III}_\lambda$}, {$\lambda\ne1$}}, journal = {Ann. of Math. (2)}, volume = {104}, number = {1}, year = {1976}, pages = {73--115}, doi = {10.2307/1971057} } @article{Haagerup1987Uniqueness, author = {Haagerup, Uffe}, title = {Connes' bicentralizer problem and uniqueness of the injective factor of type {$\mathrm{III}_1$}}, journal = {Acta Math.}, volume = {158}, number = {1-2}, year = {1987}, pages = {95--148}, doi = {10.1007/BF02392257} } @article{Ha79OVW, author = {Haagerup, Uffe}, title = {Operator valued weights in von {N}eumann algebras. {I}}, journal = {J. Funct. Anal.}, volume = {32}, number = {2}, year = {1979}, pages = {175--206}, doi = {10.1016/0022-1236(79)90053-3} } @article{ConnesTakesaki1977Flow, author = {Connes, Alain and Takesaki, Masamichi}, title = {The flow of weights on factors of type {III}}, journal = {Tohoku Math. J. (2)}, volume = {29}, number = {4}, year = {1977}, pages = {473--575}, doi = {10.2748/tmj/1178240493} } @article{GiordanoSkandalis1985, author = {Giordano, Thierry and Skandalis, Georges}, title = {Krieger factors isomorphic to their tensor square and pure point spectrum flows}, journal = {J. Funct. Anal.}, volume = {64}, number = {2}, year = {1985}, pages = {209--226}, url = {https://webusers.imj-prg.fr/~georges.skandalis/Publications/Publi10.pdf} } @article{Sekine1990Flows, author = {Sekine, Yoshihiro}, title = {Flows of weights of crossed products of type {III} factors by discrete groups}, journal = {Publ. Res. Inst. Math. Sci.}, volume = {26}, number = {4}, year = {1990}, pages = {655--666}, url = {https://ems.press/content/serial-article-files/42525} } @incollection{SutherlandTakesaki1998, author = {Sutherland, Colin E. and Takesaki, Masamichi}, title = {Right inverse of the module of approximately finite dimensional factors of type {III} and approximately finite ergodic principal measured groupoids}, booktitle = {Operator Algebras and Their Applications, II}, series = {Fields Institute Communications}, volume = {20}, year = {1998}, pages = {149--159}, publisher = {American Mathematical Society}, url = {https://dmitripavlov.org/scans/sutherland-takesaki.pdf} } @article{Popa1981Kadison, author = {Popa, Sorin}, title = {On a problem of {R. V. Kadison} on maximal abelian {$*$}-subalgebras in factors}, journal = {Invent. Math.}, volume = {65}, year = {1981}, pages = {269--281}, doi = {10.1007/BF01389015} } @article{Popa2021Ergodic, author = {Popa, Sorin}, title = {On ergodic embeddings of factors}, journal = {Comm. Math. Phys.}, volume = {384}, year = {2021}, pages = {971--996}, doi = {10.1007/s00220-020-03865-3}, eprint = {1910.06923}, archivePrefix = {arXiv}, primaryClass = {math.OA} } @incollection{Popa1985Hyperfinite, author = {Popa, Sorin}, title = {Hyperfinite subalgebras normalized by a given automorphism and related problems}, booktitle = {Operator Algebras and their Connections with Topology and Ergodic Theory}, series = {Lecture Notes in Mathematics}, volume = {1132}, year = {1985}, pages = {421--433}, publisher = {Springer}, doi = {10.1007/BFb0074899} } @article{AHHM2020Bicentralizer, author = {Ando, Hiroshi and Haagerup, Uffe and Houdayer, Cyril and Marrakchi, Amine}, title = {Structure of bicentralizer algebras and inclusions of type {III} factors}, journal = {Math. Ann.}, volume = {376}, year = {2020}, pages = {1145--1194}, doi = {10.1007/s00208-019-01939-9}, eprint = {1804.05706}, archivePrefix = {arXiv}, primaryClass = {math.OA} } @article{Marrakchi2020Full, author = {Marrakchi, Amine}, title = {Full factors, bicentralizer flow and approximately inner automorphisms}, journal = {Invent. Math.}, volume = {222}, year = {2020}, pages = {375--398}, doi = {10.1007/s00222-020-00971-w}, eprint = {1811.10253}, archivePrefix = {arXiv}, primaryClass = {math.OA} } @article{Ha78Dual, author = {Haagerup, Uffe}, title = {On the dual weights for crossed products of von {Neumann} algebras. {I}}, journal = {Math. Scand.}, volume = {43}, year = {1978}, pages = {99--118}, doi = {10.7146/math.scand.a-11768} } @incollection{Ha79Lp, author = {Haagerup, Uffe}, title = {{$L^p$}-spaces associated with an arbitrary von {Neumann} algebra}, booktitle = {Alg{\`e}bres d'op{\'e}rateurs et leurs applications en physique math{\'e}matique}, series = {Colloques Internationaux du CNRS}, volume = {274}, publisher = {CNRS}, address = {Paris}, year = {1979}, pages = {175--184}, url = {https://dmitripavlov.org/scans/haagerup.pdf} } @article{GL98, author = {Goldstein, Stanis{\l}aw and Lindsay, J. Martin}, title = {{$L^p$}-spaces and quantum dynamical semigroups}, journal = {Banach Center Publ.}, volume = {43}, year = {1998}, pages = {211--216}, url = {https://matwbn.icm.edu.pl/ksiazki/bcp/bcp43/bcp43121.pdf} } @article{GL99, author = {Goldstein, Stanis{\l}aw and Lindsay, J. Martin}, title = {Markov semigroups {KMS}-symmetric for a weight}, journal = {Math. Ann.}, volume = {313}, number = {1}, year = {1999}, pages = {39--67}, doi = {10.1007/s002080050249} } @article{VD14, author = {Van Daele, Alfons}, title = {Locally compact quantum groups. {A} von {Neumann} algebra approach}, journal = {SIGMA}, volume = {10}, year = {2014}, pages = {082}, note = {41 pp.}, doi = {10.3842/SIGMA.2014.082} } @article{Ma25, author = {Marrakchi, Amine}, title = {Kadison's problem for type {III} subfactors and the bicentralizer conjecture}, journal = {Invent. Math.}, volume = {239}, year = {2025}, pages = {79--163}, doi = {10.1007/s00222-024-01299-5}, eprint = {2308.15163}, archivePrefix = {arXiv}, primaryClass = {math.OA} } @misc{HM26, author = {Houdayer, Cyril and Marrakchi, Amine}, title = {The classification of flows on {$\mathrm{II}_1$} factors and {Connes}' bicentralizer problem}, year = {2026}, eprint = {2609.11462}, archivePrefix = {arXiv}, primaryClass = {math.OA}, doi = {10.48550/arXiv.2609.11462}, url = {https://arxiv.org/abs/2609.11462} } @misc{OAI26, author = {{OpenAI}}, title = {Expected amenable subalgebras preserving core commutants}, howpublished = {OpenAI Math Release preprint}, year = {2026}, note = {September 23, 2026}, url = {https://github.com/openai/math/blob/main/preprints/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026.pdf} }