Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T06:38:56.376Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Birtel, F. T., Banach akebras of multipliers, Duke Math. J. 28 (1961),203-212.Google Scholar
2. Birtel, F. T., Isomorphisms and isometric multipliers, Proc. Amer. Math. Soc. 13 (1962),204-209.Google Scholar
3. Helgason, S., Multipliers of Banach algebras, Ann. of Math. 64 (1956),240-254.Google Scholar
4. Ogasawara, T. and Yoshinaga, K., Weakly completely continuous Banach *-algebras, J. Sci Hiroshima Uni. Ser. A 13 (1954),15-36.Google Scholar
5. Rickart, C. E., General theory of Banach algebras, Van Nostrand, New York (1960).Google Scholar
6. Wang, J. K., Multipliers of commutative Banach algebras, Pacific J. of Math. 11 (1961), 1131-1149.Google Scholar