Finite Field Grothendieck Inequality, Finite Field Johnson-Lindenstrauss Flattening and Finite Field Bourgain-Tzafriri Restricted Invertibility Problems

Contributed by K. MAHESH KRISHNA ↗

Version 1 / Nov 05, 2026 / CC BY 4.0

Abstract

We ask for finite field versions of following three: (1) Grothendieck Inequality, (2) Johnson-Lindenstrauss Flattening Lemma, (3) Bourgain-Tzafriri Restricted Invertibility Theorem.

References

  1. Fernando Albiac and Nigel J. Kalton. Topics in B anach space theory , volume 233 of Graduate Texts in Mathematics . Springer, 2016.
  2. Ron C. Blei. An elementary proof of the G rothendieck inequality. Proc. Amer. Math. Soc. , 100(1):58--60, 1987.
  3. J. Bourgain and L. Tzafriri. Invertibility of ``large'' submatrices with applications to the geometry of B anach spaces and harmonic analysis. Israel J. Math. , 57(2):137--224, 1987.
  4. Sanjoy Dasgupta and Anupam Gupta. An elementary proof of a theorem of J ohnson and L indenstrauss. Random Structures Algorithms , 22(1):60--65, 2003.
  5. Joe Diestel, Jan H. Fourie, and Johan Swart. The metric theory of tensor products: G rothendieck's resume revisited . American Mathematical Society, Providence, RI, 2008.
  6. Simon Foucart and Holger Rauhut. A mathematical introduction to compressive sensing . Applied and Numerical Harmonic Analysis. Birkhäuser/Springer, New York, 2013.
  7. P. Frankl and H. Maehara. The J ohnson- L indenstrauss lemma and the sphericity of some graphs. J. Combin. Theory Ser. B , 44(3):355--362, 1988.
  8. Shmuel Friedland, Lek-Heng Lim, and Jinjie Zhang. An elementary and unified proof of G rothendieck's inequality. Enseign. Math. , 64(3-4):327--351, 2018.
  9. Alexandre Grothendieck. Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc. , 16, 1955.
  10. William B. Johnson and Joram Lindenstrauss. Extensions of L ipschitz mappings into a H ilbert space. Contemp. Math. , 26:189--206, 1984.
Show all 17 referencesShow fewer references
  1. J. Lindenstrauss and A. Pelczynski. Absolutely summing operators in LpL_{p} -spaces and their applications. Studia Math. , 29:275--326, 1968.
  2. Jiri Matousek. Lectures on discrete geometry , volume 212 of Graduate Texts in Mathematics . Springer-Verlag, New York, 2002.
  3. Gilles Pisier. Grothendieck's theorem, past and present. Bull. Amer. Math. Soc. (N.S.) , 49(2):237--323, 2012.
  4. Ronald E. Rietz. A proof of the G rothendieck inequality. Israel J. Math. , 19:271--276, 1974.
  5. Daniel A. Spielman and Nikhil Srivastava. An elementary proof of the restricted invertibility theorem. Israel J. Math. , 190:83--91, 2012.
  6. R. Vershynin. John's decompositions: selecting a large part. Israel J. Math. , 122:253--277, 2001.
  7. Roman Vershynin. Random sets of isomorphism of linear operators on Hilbert space. In High dimensional probability. Proceedings of the fourth international conference , pages 148--154. Beachwood, OH: IMS, Institute of Mathematical Statistics, 2006.

Version history

  1. v1 · 5 pagesSubmitted by K. MAHESH KRISHNAInitial depositCurrentNov 05, 2026