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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The dual and bidual of certain $A^{\ast }$-algebras
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by Freda E. Alexander PDF
Proc. Amer. Math. Soc. 38 (1973), 571-576 Request permission

Abstract:

It is well known that every ${B^\ast }$-algebra is Arens’ regular and that its bidual is a ${B^\ast }$-algebra. Wong has asked whether a dual ${A^\ast }$-algebra of the first kind is Arens’ regular. It is shown that this is true in the topologically simple case; in the course of the proof it is shown that in this case the bidual is, modulo its radical, an ${A^\ast }$-algebra of the first kind.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 38 (1973), 571-576
  • MSC: Primary 46L15
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0318913-1
  • MathSciNet review: 0318913