International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 3, Pages 629-636
doi:10.1155/S0161171299226294

Double multipliers on topological algebras

L. A. Khan,1 N. Mohammad,2 and A. B. Thaheem3

1Department of Mathematics, King Abdul Aziz University, P.O. Box 9028, Jeddah 21413, Saudi Arabia
2Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
3Department of Mathematical sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 17 December 1996; Revised 13 March 1998

Copyright © 1999 L. A. Khan et al. 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.

Abstract

The main purpose of this paper is to investigate some topological properties of the double multiplier algebra on a topological algebra. Let Md(A) be the double multiplier algebra on a topological algebra A, and let u and s be the uniform and strong operator topologies on Md(A), respectively. It is shown, under some additional hypotheses on A, that

(1) Md(A) is u- and s-complete;

(2) A is a u-closed two-sided ideal in Md(A);

(3) A is s-dense in Md(A);

(4) s and u have the same bounded sets;

(5) each continuous onto homomorphism ϕ:A→B has a unique extension ϕ˜:(Md(A),sA)→(Md(B),sB).