On the Lipschitz numerical index of Banach spaces

• Choi, Geunsu ^[1] ; Jung, Mingu ^[2] ; Tag, Hyung-Joon ^[3]
  1. [1] Sunchon National University

     Sunchon National University

     Corea del Sur

     
  2. [2] Korea Institute for Advanced Study

     Korea Institute for Advanced Study

     Corea del Sur

     
  3. [3] Sejong University

     Sejong University

     Corea del Sur

     

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 76, Fasc. 1, 2025, págs. 81-103
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this article, we investigate further on the Lipschitz numerical radius and index which were recently introduced. First, we provide some renorming results on Lipschitz numerical index and introduce a concept of Lipschitz numerical radius attaining maps. Namely, we observe that for any Banach space X, the set of Lipschitz numerical indices of Banach spaces which are isomorphic to X is an interval. Moreover, we show the set of Lipschitz numerical radius attaining maps is not dense in the space of Lipschitz maps vanishing at zero. Next, we discuss the Lipschitz numerical index of vector-valued function spaces, absolute sums of Banach spaces, the Köthe–Bochner spaces, and Banach spaces which contain a dense union of increasing family of one-complemented subspaces.