Resumen de On the Lipschitz numerical index of Banach spaces

Geunsu Choi, Mingu Jung, Hyung Joon Tag

• 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.