International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 75-79
doi:10.1155/S0161171297000112
Multiplication operators on weighted spaces in the non-locally convex framework
L.A. Khan1
and A.B. Thaheem2
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
Abstract
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:X→C be a mapping, f∈CV0(X,E) and define Mθ(f)=θf (pointwise). In case E is a topological algebra, ψ:X→E 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.