English

Almost square dual Banach spaces

Functional Analysis 2020-03-10 v2

Abstract

We show that finite dimensional Banach spaces fail to be uniformly non locally almost square. Moreover, we construct an equivalent almost square bidual norm on .\ell_\infty. As a consequence we get that every dual Banach space containing c0c_0 has an equivalent almost square dual norm. Finally we characterize separable real almost square spaces in terms of their position in their fourth duals.

Keywords

Cite

@article{arxiv.1912.12519,
  title  = {Almost square dual Banach spaces},
  author = {Trond A. Abrahamsen and Petr Hájek and Stanimir Troyanski},
  journal= {arXiv preprint arXiv:1912.12519},
  year   = {2020}
}

Comments

Added a new result (Theorem 3.7) that there exists an equivalent renorming of c_0 which is M-embedded and whose bidual is ASQ. Added a couple of new paragraphs and fixed some typos

R2 v1 2026-06-23T12:58:08.761Z