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International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 75-79

Multiplication operators on weighted spaces in the non-locally convex framework

1Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
2Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Mail Box 469, Dhahran 31261, Saudi Arabia

Received 13 December 1994; Revised 21 June 1995

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let X be a completely regular Hausdorff space, E a topological vector space, V a Nachbin family of weights on X, and CV0(X,E) the weighted space of continuous E-valued functions on X. Let θ:XC be a mapping, fCV0(X,E) and define Mθ(f)=θf (pointwise). In case E is a topological algebra, ψ:XE is a mapping then define Mψ(f)=ψf (pointwise). The main purpose of this paper is to give necessary and sufficient conditions for Mθ and Mψ to be the multiplication operators on CV0(X,E) where E is a general topological space (or a suitable topological algebra) which is not necessarily locally convex. These results generalize recent work of Singh and Manhas based on the assumption that E is locally convex.