On asymptotically uniformly smoothness and nonlinear geometry of Banach spaces

2018/08/09 by Bruno de Mendonça Braga, Braga, Bruno de Mendonça · 1 citation
Computer Science · Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1808.03254

openalex publication_date 2018/08/09 · openalex created_date 2018/08/22 · openalex updated_date 2026/07/28

Abstract

These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach-Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach spaces as well as weakly sequentially continuous coarse (Lipschitz) embeddings into those spaces. Some results concerning the descriptive set theoretical complexity of those properties are also obtained. We finish the paper with a list of open problem.

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