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Multiplication operators on weighted spaces of vector-valued continuous functions

Part of: Linear function spaces and their duals Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

R. K. Singh  and
Jasbir Singh Manhas
R. K. Singh
Affiliation:
University of JammuJammu 180001, India
Jasbir Singh Manhas
Affiliation:
University of JammuJammu 180001, India
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Abstract

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If V is a system of weights on a completely regular Hausdorff space X and E is alocally convex space, then CV0(X, E) and CVb (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.

MSC classification

Secondary: 47B38: Operators on function spaces (general) 46E40: Spaces of vector- and operator-valued functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 1 , February 1991 , pp. 98 - 107
Copyright
Copyright © Australian Mathematical Society 1991

References

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