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.

在本文中，我们进一步研究了最近引入的 Lipschitz 数值半径和指数。首先，我们提供了Lipschitz数值指数的一些重整结果，并引入了Lipschitz数值半径获得图的概念。也就是说，我们观察到对于任何 Banach 空间X ，与X同构的 Banach 空间的 Lipschitz 数值索引的集合是一个区间。此外，我们证明了利普希茨数值半径获得图集在利普希茨图消失为零的空间中并不密集。接下来，我们讨论向量值函数空间的 Lipschitz 数值索引、Banach 空间的绝对和、Köthe-Bochner 空间以及包含一补子空间递增族的密集并集的 Banach 空间。