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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
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.

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

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Keywords: Direct integral decomposition, antisymmetric operator algebra, antisymmetric projection, atom of a measure
Article copyright: © Copyright 1986 American Mathematical Society

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