Multipliers for some spaces of Banach algebra valued functions
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).
continuous functions on locally compact Abelian group
scientific article; zbMATH DE number 3916956