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Multipliers for some spaces of Banach algebra valued functions. (English) Zbl 0574.43003
Let G be a locally compact Abelian group and A be a commutative Banach algebra. Let $C\sb 0(G,A)$ 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 $C\sb 0(G,A)$ is isometrically isomorphic to $C\sp b(G,M(A))$, the bounded continuous M(A)-valued functions on G; (ii) the L’(G,A)-module homomorphisms of $C\sb 0(G,A)$ are isometrically isomorphic with M(G,A).
Reviewer: H.Vasudeva

MSC:
43A22Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
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