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A characterization of dual $ B^{\ast} $-algebras


Author: Edith A. McCharen
Journal: Proc. Amer. Math. Soc. 37 (1973), 84
MSC: Primary 46K05
DOI: https://doi.org/10.1090/S0002-9939-1973-0306927-7
MathSciNet review: 0306927
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Abstract: Let A be a $ {B^\ast}$-algebra. The second conjugate space of A, denoted by $ {A^{ \ast \ast }}$, is a $ {B^\ast}$-algebra under the Arens multiplication. A new proof is given that A is a dual algebra if and only if the natural image of A in $ {A^{ \ast \ast }}$ is an ideal in $ {A^{\ast \ast}}$.


References [Enhancements On Off] (What's this?)

  • [1] B. J. Tomiuk and Pak-Ken Wong, The Arens product and duality in $ {B^\ast}$-algebras, Proc. Amer. Math. Soc. 25 (1970), 529-535. MR 41 #4256. MR 0259620 (41:4256)
  • [2] J. Dixmier, Les $ {C^\ast}$-algèbres et leurs représentations, 2ième éd., Cahiers Scientifiques, fasc. 29, Gauthier-Villars, Paris, 1969. MR 39 #7442. MR 0246136 (39:7442)
  • [3] R. E. Edwards, Functional analysis. Theory and applications, Holt, Rinehart and Winston, New York, 1965. MR 36 #4308. MR 0221256 (36:4308)

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DOI: https://doi.org/10.1090/S0002-9939-1973-0306927-7
Article copyright: © Copyright 1973 American Mathematical Society

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