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Isomorphisms of multiplier algebras

Published online by Cambridge University Press:  18 May 2009

B. J. Tomiuk
B. J. Tomiuk
Affiliation:
Department of Mathematics, University of Ottawa, Ottawa, Ottawa KIN 9B4, Canada
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Let A and B be semisimple Banach algebras, and let M1(A) (resp. M1(B)) be the algebra of left multipliers on A (resp. B). Suppose that A is an abstract Segal algebra in B. We find conditions on A and B which imply that M1(A) is topologically algebra isomorphic to M1(B). As a special case we obtain the result of [8] which states that if A is an A*-algebra that is a*-ideal in its B*-algebra completion B and A2 is dense in A then M1(A) is topologically algebra isomorphic to M1(B). We make an application of our main result to right complemented Banach algebras.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 1 , January 1986 , pp. 73 - 77
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

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