Multipliers of Modules of Continuous Vector-Valued Functions

Abstract

In 1961, Wang showed that if A is the commutative C*-algebra C0(X) with X a locally compact Hausdorff space, then M(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing that HomC0(X,A)(C0(X,E),C0(X,F))≃Cs,b(X,HomA(E,F)), where E and F are p-normed spaces which are also essential isometric left A-modules with A being a certain commutative F-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.