Double Multipliers on Topological Algebras
نویسندگان
چکیده
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 uand 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 homomorphismφ :A→ B has a unique extension φ̃ : (Md(A), sA)→ (Md(B),sB).
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