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. Khan1
, N. Mohammad2
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
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).