## Abstract and Applied Analysis

### Multipliers of Modules of Continuous Vector-Valued Functions

#### Abstract

In 1961, Wang showed that if $A$ is the commutative ${C}^{\mathrm{\ast}}$-algebra ${C}_{\mathrm{0}}(X)$ with $X$ a locally compact Hausdorff space, then $M({C}_{\mathrm{0}}(X))\cong {C}_{b}(X)$. 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 $\text{H}\text{o}{\text{m}}_{{C}_{\mathrm{0}}(X,A)}({C}_{\mathrm{0}}(X,E),{C}_{\mathrm{0}}(X,F))\simeq {C}_{s,b}(X,\text{H}\text{o}{\text{m}}_{A}(E,F)),$ 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 397376, 6 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606519

Digital Object Identifier
doi:10.1155/2014/397376

Mathematical Reviews number (MathSciNet)
MR3212422

Zentralblatt MATH identifier
07022313

#### Citation

Khan, Liaqat Ali; Alsulami, Saud M. Multipliers of Modules of Continuous Vector-Valued Functions. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 397376, 6 pages. doi:10.1155/2014/397376. https://projecteuclid.org/euclid.aaa/1412606519

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