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The Daugavet Property of Bidual Spaces

A mix of human-written and AI-generated textHuman understanding: all partsmath.FA — Functional Analysis

Contributed by Samir Hamad ↗

Version 1 / Nov 11, 2026 / CC BY 4.0

Abstract

We construct a separable Banach space whose bidual has the Daugavet property. The construction proceeds by successively extending finite-dimensional spaces so that prescribed vectors are approximated by averages of newly added unit vectors. A simultaneous extension argument produces finitely many fixed functionals whose norm-attaining faces approximate the unit ball of the bidual.

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References

  1. A. M. Plichko and M. M. Popov, Some open problems on Banach spaces , Mat. Stud. 38 (2012), no. 2, 203--211. https://aplichko.orgfree.com/pdf/120.pdf.link
  2. S. Hamad, Tensor Products and the Isomorphic Theory of Daugavet Spaces , preprint (2026), arXiv:2611.02060. https://arxiv.org/abs/2611.02060.arXiv
  3. V. M. Kadets, R. V. Shvidkoy, G. G. Sirotkin and D. Werner, Banach spaces with the Daugavet property , Trans. Amer. Math. Soc. 352 (2000), 855--873.

Version history

  1. v1 · 6 pagesSubmitted by Samir HamadInitial depositCurrentNov 10, 2026