Convex-transitivity of Banach algebras via ideals

TL;DR

This paper presents a method to construct convex-transitive Banach spaces by quotienting to remove asymmetries, focusing on Banach algebras and their ideals, and explores convex-transitivity in ultraproducts and tensor products.

Contribution

It introduces a novel quotient-based approach to produce convex-transitive Banach spaces and analyzes their properties in ultraproducts and tensor products.

Findings

Successfully constructs convex-transitive Banach spaces via quotients.

Shows convex-transitivity extends to ultraproducts of Banach spaces.

Establishes convex-transitivity in tensor products of Banach spaces.

Abstract

We investigate a method for producing concrete convex-transitive Banach spaces. The gist of the method is in getting rid of dissymmetries of a given space by taking a carefully chosen quotient. The spaces of interest here are typically Banach algebras and their ideals. We also investigate the convex-transitivity of ultraproducts and tensor products of Banach spaces.