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 has the diagonal of this algebra as the algebra of diagonalizable operators if and only if almost all direct integrands of are antisymmetric algebras. By using the antisymmetric decomposition a direct integral model of a commutative, reflexive algebra is obtained.

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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