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The separable Jung constant in Banach spaces

Volume 258 / 2021

Jesús M. F. Castillo, Pier Luigi Papini Studia Mathematica 258 (2021), 157-173 MSC: 46B04, 46B20, 46B26, 46M18. DOI: 10.4064/sm190812-11-5 Published online: 20 November 2020

Abstract

This paper contains a study of the separable version $J_s(\cdot )$ of the classical Jung constant. We first establish, following Davis (1977), that a Banach space $X$ is $1$-separably injective if and only if $J_s(X)=1$. This characterization is then used for the understanding of new $1$-separably injective spaces. The last section establishes the inequality $\frac {1}{2}K(Y)J_s(X)\leq e_1^s(Y,X)$ connecting the separable Jung constant, Kottman’s constant and the separable-one-point extension constant for Lipschitz maps, which is then used to derive an improved version of Kalton’s inequality $K(X,c_0)\leq e(X,c_0)$ and a new characterization of $1$-separable injectivity.

Authors

  • Jesús M. F. CastilloInstituto de Matemáticas
    de la Universidad de Extremadura
    Avenida de Elvas
    06071 Badajoz, Spain
    e-mail
  • Pier Luigi PapiniVia Martucci 19
    40136 Bologna, Italy
    e-mail

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