Uniformly convex-transitive function spaces
Fernando Rambla-Barreno, Jarno Talponen

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.
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Fixed Point Theorems Analysis
