Convex-transitivity and function spaces

2007/11/23 by Jarno Talponen, Talponen, Jarno
Mathematics · #46B04 #46E40 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #math.FA #msc:46B04 #msc:46E40

paper · pdf · doi:10.48550/arxiv.0711.3768

Corrected version

openalex publication_date 2007/11/23 · arxiv created 2008/01/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If X is a convex-transitive Banach space and 1≤ p≤ ∞ 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 C₀(L) is convex-transitive, then C₀(L,H) is convex-transitive. Some new fairly concrete examples of convex-transitive spaces are provided.

Related

• Uniformly convex-transitive function spaces
• Convex-transitive characterizations of Hilbert spaces
• Convex-transitivity of Banach algebras via ideals
• Characterization of Hilbertizable spaces via convex functions
• B-convex operator spaces