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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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On the characterization of Abelian $W^{^{\ast } }$-algebras
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by J. W. Jenkins PDF
Proc. Amer. Math. Soc. 35 (1972), 436-438 Request permission

Abstract:

In this note we present an elementary proof that an Abelian ${W^ \ast }$-algebra is generated by the range of some real spectral measure.
References
  • Jacques Dixmier, Les algèbres d’opĂ©rateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers Scientifiques, Fasc. XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722
    • M. A. NaÄ­mark, Normed rings, GITTL, Moscow, 1956; English transl., Noordhoff, Groningen, 1959. MR 19, 870; MR 22 #1824.
  • J. T. Schwartz, $W^{\ast }$-algebras, Gordon and Breach Science Publishers, New York-London-Paris, 1967. MR 0232221
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 436-438
  • MSC: Primary 46L10
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0306934-3
  • MathSciNet review: 0306934