A Note on the class of superreflexive almost transitive Banach spaces

TL;DR

This paper characterizes the class J of Banach spaces that are simultaneously almost transitive, uniformly convex, and uniformly smooth, using convex-transitivity and weak geometric properties of the norm.

Contribution

It provides a new characterization of the class J of superreflexive almost transitive Banach spaces based on geometric and transitivity properties.

Findings

Characterization of class J in terms of convex-transitivity.

Connection between weak geometry and almost transitivity.

Insight into the structure of superreflexive Banach spaces.

Abstract

The class J of simultaneously almost transitive, uniformly convex and uniformly smooth Banach spaces is characterized in terms of convex-transitivity and weak geometry of the norm.