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Proceedings of the American Mathematical Society

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The dual and bidual of certain $ A\sp{\ast} $-algebras


Author: Freda E. Alexander
Journal: Proc. Amer. Math. Soc. 38 (1973), 571-576
MSC: Primary 46L15
MathSciNet review: 0318913
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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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DOI: https://doi.org/10.1090/S0002-9939-1973-0318913-1
Keywords: $ {A^\ast}$-algebra, annihilator algebra, Arens regular
Article copyright: © Copyright 1973 American Mathematical Society