Almost squareness and strong diameter two property in tensor product spaces

TL;DR

This paper investigates how almost squareness and the strong diameter two property behave in projective tensor product spaces, providing new examples and extending existing results in Banach space theory.

Contribution

It demonstrates that almost squareness is preserved under projective tensor products and offers new conditions for the strong diameter two property in symmetric tensor products.

Findings

Almost squareness is preserved in projective tensor products.

New sufficient conditions for strong diameter two property are established.

Provides novel examples of tensor product spaces with these properties.

Abstract

We study almost squareness and the strong diameter two property in the setting of projective (symmetric) tensor product. We prove that almost squareness is preserved by taking projective tensor product, providing non-trivial examples of ASQ projective tensor product spaces. Furthermore, we give sufficient conditions for a projective symmetric tensor product to have the strong diameter two property which extend most of the known results and provide new examples of such spaces with the strong diameter two property.