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 L. A. Khan and A. B. Thaheem. 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 be a completely regular Hausdorff space, a topological vector space, a
Nachbin family of weights on , and the weighted space of continuous -valued functions
on . Let be a mapping, and define (pointwise). In case is
a topological algebra, is a mapping then define (pointwise). The main purpose
of this paper is to give necessary and sufficient conditions for and to be the multiplication
operators on where 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 is locally convex.