ABSTRACT

In this paper, we study the relationship between numerical index of a Banach space E and the numerical index of a class of subspaces of $\mathcal{C}(\mathrm{\Omega },E)$, the space of all continuous E-valued functions defined on a compact Hausdorff topological space Ω. The subspaces considered, satisfy an invariance condition and a norm attaining condition proposed by J. Jamison. As a consequence, we prove that the numerical indices of several classes of vector-valued function spaces are less than or equal to the numerical index of the respective range spaces.

中文翻译：

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向量值函数空间的数值索引

摘要

本文研究了 Banach 空间E的数值索引与$\mathcal{C}(\mathrm{\Omega },乙)$,定义在紧凑 Hausdorff 拓扑空间 Ω 上的所有连续E值函数的空间。所考虑的子空间满足 J. Jamison 提出的不变条件和范数获得条件。因此，我们证明了几类向量值函数空间的数值索引小于或等于各自范围空间的数值索引。