J Austral Math Soc Ser A 50 pp98--107, 1991.

Multiplication Operators on Weighted Spaces of Vector-Valued Continuous Functions

R. K. Singh and Jasbir Singh Manhas

(Received 5 June 1989)

Abstract

If V is a system of weights on a completely regular Hausdorff space X and E is a locally concex space, then CV₀(X, E) and CV_b(X, E) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.

1980 AMS Subject Classification (1985 Revision): 47B38, 46E40

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Authors

R. K. Singh
Jasbir Singh Manhas: University of Jammu, Jammu 180001, India.

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Last Modified: Mon Feb 3 9:46:10 2003