Analytic operator algebras (factorization and an expectation)

Author:
Baruch Solel

Journal:
Trans. Amer. Math. Soc. **287** (1985), 799-817

MSC:
Primary 47D25; Secondary 46L99

DOI:
https://doi.org/10.1090/S0002-9947-1985-0768742-2

MathSciNet review:
768742

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a -finite von Neumann algebra and a periodic flow on . The algebra of analytic operators in is and is denoted . We prove that every invertible operator can be written as , where is unitary in and . We also prove inner-outer factorization results for .

Another result represents as the image of a certain nest subalgebra (of a von Neumann algebra that contains ) via a conditional expectation. As corollaries we prove a distance formula and an interpolation result for the case where is an injective von Neumann algebra.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0768742-2

Keywords:
Flow,
analytic operators with respect to a flow,
inner-outer factorization,
expectation,
distance estimate,
interpolation

Article copyright:
© Copyright 1985
American Mathematical Society