Multipliers for some spaces of Banach algebra valued functions
type: Item
instance of: scholarly article
title: Multipliers for some spaces of Banach algebra valued functions
zbMATH Open document ID: 0574.43003
DOI: 10.1216/RMJ-1985-15-1-157
published in: Rocky Mountain Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Let G be a locally compact Abelian group and A be a commutative Banach algebra. Let \(C_ 0(G,A)\) denote the space of A-valued continuous functions on G vanishing at infinity and L'(G,A) denote the Banach algebra of A-valued Bochner integrable functions on G. M(A) will denote the algebra of multipliers of A and M(G,A) will denote A-valued regular Borel measures of bounded variation on G. The following two results have been proved: (i) The space of algebra multipliers of \(C_ 0(G,A)\) is isometrically isomorphic to \(C^ b(G,M(A))\), the bounded continuous M(A)-valued functions on G; (ii) the L'(G,A)-module homomorphisms of \(C_ 0(G,A)\) are isometrically isomorphic with M(G,A).
Mathematics Subject Classification ID: 43A22
zbMATH DE Number: 3916956
zbMATH Keywords: continuous functions on locally compact Abelian group
zbMATH Keywords: Banach algebra
zbMATH Keywords: Bochner integrable functions
zbMATH Keywords: regular Borel measures
zbMATH Keywords: algebra multipliers
author: Hang-Chin Lai
reviewed by: Harkrishan L. Vasudeva
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3916956