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Analytic Subalgebras of Von Neumann Algebras

Published online by Cambridge University Press:  20 November 2018

Paul S. Muhly  and
Kichi-Suke Saito
Paul S. Muhly
Affiliation:
The University of Iowa,Iowa City, Iowa
Kichi-Suke Saito
Affiliation:
The University of Iowa,Iowa City, Iowa Niigata University, Niigata, Japan
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Let M be a von Neumann algebra and let {αt}t∊R be a σ-weakly continuous flow on M; i.e., suppose that {αt}t∊R is a one-parameter group of *-automorphisms of M such that for each ρ in the predual, M∗, of M and for each x ∊ M, the function of t, ρ(αt(x)), is continuous on R. In recent years, considerable attention has been focused on the subspace of M, H∞(α), which is defined to be

where H∞(R) is the classical Hardy space consisting of the boundary values of functions bounded analytic in the upper half-plane. In Theorem 3.15 of [8] it is proved that in fact H∞(α) is a σ-weakly closed subalgebra of M containing the identity operator such that

is σ-weakly dense in M, and such that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 1 , 01 February 1987 , pp. 74 - 99
Copyright
Copyright © Canadian Mathematical Society 1987

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