Uniformly convex-transitive function spaces

TL;DR

This paper introduces the concept of uniform convex-transitivity in Banach spaces, explores its properties, provides examples, and discusses its implications for Banach-valued function spaces, leading to new convex-transitive space examples.

Contribution

It defines a new property of Banach spaces called uniform convex-transitivity and demonstrates its usefulness in constructing and understanding convex-transitive spaces.

Findings

Introduces uniform convex-transitivity property.

Provides examples of uniformly convex-transitive spaces.

Connects this property with Banach-valued function spaces.

Abstract

We introduce a property of Banach spaces called uniform convex-transitivity, which falls between almost transitivity and convex-transitivity. We will provide examples of uniformly convex-transitive spaces. This property behaves nicely in connection with some Banach-valued function spaces. As a consequence, we obtain new examples of convex-transitive Banach spaces.