Numerical index of vector-valued function spaces

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 (Formula presented.), 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.

Publication Title

Linear and Multilinear Algebra

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