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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Antisymmetry and the direct integral decomposition of unstarred operator algebras


Author: Wacław Szymański
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0822448-6
Keywords: Direct integral decomposition, antisymmetric operator algebra, antisymmetric projection, atom of a measure
Article copyright: © Copyright 1986 American Mathematical Society