Double multipliers on topological algebras

L. A. Khan, N. Mohammad and A. B. Thaheem

International Journal of Mathematics and Mathematical Sciences, 1999, vol. 22, 1-8

Abstract:

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

(1) M d ( A ) is u - and s -complete;

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

(3) A is s -dense in M d ( A ) ;

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

(5) each continuous onto homomorphism ϕ : A → B has a unique extension ϕ ˜ : ( M d ( A ) , s A ) → ( M d ( B ) , s B ) .

Date: 1999
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:815389

DOI: 10.1155/S0161171299226294

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