Abstract and Applied Analysis

Multipliers of Modules of Continuous Vector-Valued Functions

Liaqat Ali Khan and Saud M. Alsulami

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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.

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

First available in Project Euclid: 6 October 2014

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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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