Asymptotic structure of free product von Neumann algebras
2016 ◽
Vol 161
(3)
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pp. 489-516
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Keyword(s):
AbstractLet (M, ϕ) = (M1, ϕ1) * (M2, ϕ2) be the free product of any σ-finite von Neumann algebras endowed with any faithful normal states. We show that whenever Q ⊂ M is a von Neumann subalgebra with separable predual such that both Q and Q ∩ M1 are the ranges of faithful normal conditional expectations and such that both the intersection Q ∩ M1 and the central sequence algebra Q′ ∩ Mω are diffuse (e.g. Q is amenable), then Q must sit inside M1. This result generalizes the previous results of the first named author in [Ho14] and moreover completely settles the questions of maximal amenability and maximal property Gamma of the inclusion M1 ⊂ M in arbitrary free product von Neumann algebras.
2016 ◽
Vol 152
(12)
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pp. 2461-2492
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Keyword(s):
2013 ◽
Vol 150
(1)
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pp. 143-174
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2002 ◽
Vol 13
(01)
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pp. 31-41
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2013 ◽
Vol 265
(12)
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pp. 3305-3324
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1990 ◽
Vol 92
(1)
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pp. 77-91
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2008 ◽
Vol 19
(04)
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pp. 481-501
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