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On the characterization of Abelian $ W\sp{\sp{\ast} }$-algebras


Author: J. W. Jenkins
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
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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 [Enhancements On Off] (What's this?)

  • [1] Jacques Dixmier, Les algèbres d’opérateurs dans l’espace hilbertien (Algèbres de von Neumann), Cahiers scientifiques, Fascicule XXV, Gauthier-Villars, Paris, 1957 (French). MR 0094722
  • [2] M. A. Naĭmark, Normed rings, GITTL, Moscow, 1956; English transl., Noordhoff, Groningen, 1959. MR 19, 870; MR 22 #1824.
  • [3] J. T. Schwartz, 𝑊*-algebras, Gordon and Breach Science Publishers, New York-London-Paris, 1967. MR 0232221

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0306934-3
Keywords: Abelian $ {W^\ast}$-algebras, spectral measure, lattice of projections, chain of projections
Article copyright: © Copyright 1972 American Mathematical Society