The dual and bidual of certain 𝐴*-algebras

Alexander, Freda E.

doi:10.1090/S0002-9939-1973-0318913-1

The dual and bidual of certain $A^{\ast }$-algebras
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by Freda E. Alexander

Proc. Amer. Math. Soc. 38 (1973), 571-576

DOI: https://doi.org/10.1090/S0002-9939-1973-0318913-1

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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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