On Asymptotic Transitivity in Banach Spaces

2006/10/18 by Jarno Talponen, J. Talponen, Talponen, J.
Mathematics · #46B04 #46C15 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46B04 #msc:46C15

paper · pdf · doi:10.48550/arxiv.math/0610547

15 pages

openalex publication_date 2006/10/18 · arxiv created 2006/11/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a flexible almost isometric version of the almost transitivity property of Banach spaces. With the help of this new notion we generalize to several directions a strong recent rotational characterization of Hilbert spaces due to Randrianantoanina. This characterization is a partial answer to the classical Banach-Mazur rotation problem.

Citations

• The Amalgamation Property in Classical Lebesgue-Riesz Spaces, Banach Spaces with Transitive and Almost Transitive Norms and Projection Constants

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• A note on Banach--Mazur problem
• Convex-transitive characterizations of Hilbert spaces
• On Mazur rotations problem and its multidimensional versions
• On an isomorphic Banach-Mazur rotation problem and maximal norms in Banach spaces
• Directionally Euclidean Structures of Banach Spaces