Multipliers of Modules of Continuous Vector-Valued Functions

Abstract EN

In 1961, Wang showed that if A is the commutative C * -algebra C 0 ( X ) with X a locally compact Hausdorff space, then M ( C 0 ( X ) ) ≅ C b ( 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 H o m C 0 ( X , A ) ( C 0 ( X , E ) , C 0 ( X , F ) ) ≃ C s , b ( X , H o m A ( 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.