ON OUTER AUTOMORPHISM GROUPS OF FREE PRODUCT FACTORS

2002 ◽  
Vol 13 (01) ◽  
pp. 31-41 ◽  
Author(s):  
JAESEONG HEO
Keyword(s):  
Free Product ◽  
Von Neumann Algebras ◽  
Automorphism Groups ◽  
Outer Automorphism ◽  
Type Ii ◽  
Von Neumann ◽  
Property T ◽  
Outer Automorphism Groups ◽  
Finite Von Neumann Algebras ◽  
Tracial States

In this paper, we answer the Dixmier's question for type II 1-factors with property T in the negative, that is, if G is a discrete i.c.c group with property T of Kazhdan, L(G) is not isomorphic to [Formula: see text] for any factor [Formula: see text] of type II 1. To prove this, we study outer automorphism groups on a free product of two finite von Neumann algebras with respect to tracial states.

scholarly journals Asymptotic structure of free product von Neumann algebras

2016 ◽  
Vol 161 (3) ◽  
pp. 489-516 ◽  
Author(s):  
CYRIL HOUDAYER ◽  
YOSHIMICHI UEDA
Keyword(s):  
Free Product ◽  
Von Neumann Algebras ◽  
Asymptotic Structure ◽  
Von Neumann ◽  
Central Sequence ◽  
Separable Predual ◽  
Conditional Expectations ◽  
Sequence Algebra ◽  
Normal States ◽  
Finite Von Neumann Algebras

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.

scholarly journals ON EQUALITY CONDITION FOR TRACE JENSEN INEQUALITY IN SEMI-FINITE VON NEUMANN ALGEBRAS

2008 ◽  
Vol 19 (04) ◽  
pp. 481-501 ◽  
Author(s):  
TETSUO HARADA ◽  
HIDEKI KOSAKI
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Adjoint Operator ◽  
Strict Convexity ◽  
Jensen Inequality ◽  
Von Neumann ◽  
Convexity Assumption ◽  
Finite Von Neumann Algebra ◽  
Equality Condition ◽  
Finite Von Neumann Algebras

Let τ be a faithful semi-finite normal trace on a semi-finite von Neumann algebra, and f(t) be a convex function with f(0) = 0. The trace Jensen inequality states τ(f(a* xa)) ≤ τ(a* f(x)a) for a contraction a and a self-adjoint operator x. Under certain strict convexity assumption on f(t), we will study when this inequality reduces to the equality.

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