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Multipliers of Modules of Continuous Vector‐Valued Functions

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  • Liaqat Ali Khan
  • Saud M. Alsulami

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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:397376
DOI: 10.1155/2014/397376
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