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Does the theory of tracial von Neumann algebras have a model companion?
the theory of tracial von Neumann algebras model companion Logic
2012/7/11
In this note, we show that, assuming a positive solution to the Connes Embedding Problem (CEP), the theory of tracial von Neumann algebras does not have a model companion. This will follow from the fa...
We will introduce the Rohlin property for flows on von Neumann algebras and classify them up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as ...
Cartan MASAs in von Neumann Algebras are Norming and a New Proof of Mercer's Theorem
Norming algebra Cartan MASA C*-diagonal
2012/3/1
In this note we observe that a result of Sinclair and Smith together with the Feldman-Moore description of a von Neumann algebra with a Cartan MASA shows that Cartan MASAs are norming. We also use the...
Topologies on Central Extensions of Von Neumann Algebras
Von Neumann Algebras Topologies Operator Algebras
2011/9/21
Abstract: Given a von Neumann algebra $M$ we consider the central extension $E(M)$ of $M.$ We introduce the topology $t_c(M)$ on $E(M)$ generated by a center-valued norm and prove that it coincides wi...
On commutative, operator amenable subalgebras of finite von Neumann algebras
On commutative operator amenable subalgebras finite von Neumann algebras
2011/2/23
An open question, raised independently by several authors, asks if a closed amenable subalgebra of B(H) must be similar to an amenable C-algebra; the question remains open
even for singly-generated ...
Freeness of Linear and Quadratic Forms in von Neumann Algebras
Free random variables free convolutions a characterization of the semicircle law
2011/2/28
We characterize the semicircular distribution by freeness of linear and qua-dratic forms in noncommutative random variables from tracial W-probability spaces with relaxed moment conditions.
Factoriality, type classification and fullness for free product von Neumann algebras
Factoriality type classification von Neumann algebras
2010/11/24
We give a complete answer to the questions of factoriality, type classification and fullness for arbitrary free product von Neumann algebras
On the Relative Weak Asymptotic Homomorphism Property for Pairs of Groups von Neumann Algebras
the Relative Weak Asymptotic Homomorphism Property Pairs Groups von Neumann Algebras
2010/11/9
We provide a direct and elementary proof of the equivalence between the weak asymptotic homomorphism property for the pair of group von Neumann algebras $L(H)\subset L(G)$ and the embedding into $H$ ...
Factorization and dilation problems for completely positive maps on von Neumann algebras
Factorization dilation problems for completely positive maps von Neumann algebras
2010/11/29
We study factorization and dilation properties of Markov maps between von Neumann algebras
equipped with normal faithful states, i.e., completely positive unital maps which preserve the
given states...
On Monotone product of von Neumann algebras
factor von Neumann algebras monotone product $C^\ast$-algebras GNS construction
2007/12/11
In this note, we give complete descriptions of the structure of the monotone product of two von Neumann algebras and two $C^\ast$-algebras. We show that the monotone product of two simple von Neumann ...
A Property of Weak Convergence of Positive Contractions of Von Neumann Algebras
Positive contraction mixing completely mixing von Neumann algebra
2010/2/26
In the present paper we prove that the mixing property of positive L1-contraction of finite von Neumann algebras implies the property of complete mixing.