Nonlinear weakly sequentially continuous embeddings between Banach spaces

2017/10/21 by Bruno de Mendonça Braga, Braga, Bruno de Mendonça
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1710.07852

openalex publication_date 2017/10/21 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

In these notes, we study nonlinear embeddings between Banach spaces which are also weakly sequentially continuous. In particular, our main result implies that if a Banach space X coarsely (resp. uniformly) embeds into a Banach space Y by a weakly sequentially continuous map, then every spreading model (e_n)_n of a normalized weakly null sequence in X satisfies ‖e₁+…+e_k‖_δY\lesssim‖e₁+…+e_k‖_S, where δ_Y is the modulus of asymptotic uniform convexity of Y. Among other results, we obtain Banach spaces X and Y so that X coarsely (resp. uniformly) embeds into Y, but so that X cannot be mapped into Y by a weakly sequentially continuous coarse (resp. uniform) embedding.

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