Some results on almost square Banach spaces

TL;DR

This paper characterizes almost square Banach spaces as those containing an isomorphic copy of c_0 and explores their tensor products, revealing they have the strong diameter two property.

Contribution

It establishes a topological characterization of almost square Banach spaces and analyzes the diameter properties of their tensor products.

Findings

Banach spaces with an equivalent ASQ norm contain an isomorphic c_0

Symmetric projective tensor products of ASQ spaces have the strong diameter two property

Provides a topological perspective on almost square Banach spaces

Abstract

We study almost square Banach spaces under a topological point of view. Indeed, we prove that the class of Banach spaces which admits an equivalent norm to be ASQ is that of those Banach spaces which contain an isomorphic copy of $c_0$. We also prove that the symmetric projective tensor products of an almost square Banach space have the strong diameter two property