Generalized Numerical Index of Function Algebras

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Abstract

Let X be a complex Banach space and Cb(Ω:X) be the Banach space of all bounded continuous functions from a Hausdorff space Ω to X, equipped with sup norm. A closed subspace A of Cb(Ω:X) is said to be an X-valued function algebra if it satisfies the following three conditions: (i) A{x°f:fA, xX} is a closed subalgebra of Cb(Ω), the Banach space of all bounded complex-valued continuous functions; (ii) φ⊗xA for all φA and xX; and (iii) φfA for every φA and for every fA. It is shown that k-homogeneous polynomial and analytic numerical index of certain X-valued function algebras are the same as those of X.

Original languageEnglish
Article number9080867
JournalJournal of Function Spaces
Volume2019
DOIs
StatePublished - 2019

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