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Transactions of the American Mathematical Society

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A reduction theory for non-self-adjoint operator algebras

Authors: E. A. Azoff, C. K. Fong and F. Gilfeather
Journal: Trans. Amer. Math. Soc. 224 (1976), 351-366
MSC: Primary 46L15; Secondary 47A15
MathSciNet review: 0448109
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Abstract: It is shown that every strongly closed algebra of operators acting on a separable Hilbert space can be expressed as a direct integral of irreducible algebras. In particular, every reductive algebra is the direct integral of transitive algebras. This decomposition is used to study the relationship between the transitive and reductive algebra problems. The final section of the paper shows how to view direct integrals of algebras as measurable algebra-valued functions.

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Keywords: Direct integral of algebras, transitive algebra, reductive algebra, Borel structure
Article copyright: © Copyright 1976 American Mathematical Society