Analytic Subalgebras of Von Neumann Algebras
1987 ◽
Vol 39
(1)
◽
pp. 74-99
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Keyword(s):
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 bewhere 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 thatis σ-weakly dense in M, and such that
1985 ◽
Vol 37
(3)
◽
pp. 405-429
◽
1984 ◽
Vol 25
(1)
◽
pp. 19-25
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Keyword(s):
1988 ◽
Vol 40
(1)
◽
pp. 248-256
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Keyword(s):
1977 ◽
Vol 81
(2)
◽
pp. 233-236
◽
1978 ◽
Vol 84
(1)
◽
pp. 47-56
◽
Keyword(s):
2008 ◽
Vol 19
(04)
◽
pp. 481-501
◽
2006 ◽
Vol 58
(4)
◽
pp. 768-795
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