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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Antisymmetry and the direct integral decomposition of unstarred operator algebras
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by Wacław Szymański PDF
Proc. Amer. Math. Soc. 96 (1986), 497-501 Request permission

Abstract:

It is shown that the direct integral decomposition of a non-self-adjoint operator algebra ${\mathcal A}$ has the diagonal ${\mathcal A} \cap {{\mathcal A}^ * }$ of this algebra as the algebra of diagonalizable operators if and only if almost all direct integrands of ${\mathcal A}$ are antisymmetric algebras. By using the antisymmetric decomposition a direct integral model of a commutative, reflexive algebra is obtained.
References
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 96 (1986), 497-501
  • MSC: Primary 47D25; Secondary 46L45
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0822448-6
  • MathSciNet review: 822448