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A Note on Isomorphisms of Multiplier Algebras

Published online by Cambridge University Press:  20 November 2018

Pak-Ken Wong
Pak-Ken Wong*
Affiliation:
Department of Mathematics, Seton Hail University, South Orange, New Jersey, 07079
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Let A1, A2 be commutative semi-simple Banach algebras and M(A1), M(A2) their multiplier algebras. Birtel in [2] has proved that every isomorphism of A1 onto A2 induces an isomorphism of M(A1) onto M(A2). In this note, we extend this result to the noncommutative case. We also show that if A is a dual A*-algebra which is a dense two-sided ideal of a B*-algebra B, then M(A) is isomorphic to M(B). Thus the converse of the previous result cannot hold. All algebras under consideration are over the complex field.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 2 , 01 June 1979 , pp. 243 - 245
Copyright
Copyright © Canadian Mathematical Society 1979

References

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