Convex-transitivity and function spaces

TL;DR

This paper explores the properties of convex-transitive Banach spaces and demonstrates that certain function space constructions preserve convex-transitivity, providing new concrete examples of such spaces.

Contribution

It establishes that the closed linear span of simple functions in Bochner spaces retains convex-transitivity and offers new concrete examples of convex-transitive spaces.

Findings

The span of simple functions in L^p([0,1],X) is convex-transitive.

C_0(L,H) is convex-transitive when H is an infinite-dimensional Hilbert space.

Provides new concrete examples of convex-transitive spaces.

Abstract

If X is a convex-transitive Banach space and 1\leq p\leq \infty then the closed linear span of the simple functions in the Bochner space L^{p}([0,1],X) is convex-transitive. If H is an infinite-dimensional Hilbert space and C_{0}(L) is convex-transitive, then C_{0}(L,H) is convex-transitive. Some new fairly concrete examples of convex-transitive spaces are provided.