The starting points for this paper are simple descriptions of the norm and strong* closures of the unitary orbit of a normal operator in a von Neumann algebra. The statements are in terms of spectral data and do not depend on the type or cardinality of the algebra. We relate this to several known results and derive some consequences, of which we list a few here. Exactly when the ambient von Neu...

The invariant subspace problem relative to a von Neumann algebra M ⊆ B(H) asks whether every operator T ∈ M has a proper, nontrivial invariant subspace H0 ⊆ H such that the orthogonal projection p onto H0 is an element of M; equivalently, it asks whether there is a projection p ∈ M, p / ∈ {0, 1}, such that Tp = pTp. Even when M is a II1–factor, this invariant subspace problem remains open. In t...

In this paper we describe the structure of all sequential isomorphisms between the sets of von Neumann algebra effects. It turns out that if the underlying algebras have no commutative direct summands, then every sequential isomorphism between the sets of their effects extends to the direct sum of a *-isomorphism and a *-antiisomorphism between the underlying von Neumann algebras.

We obtain a characterization of property (T) for von Neumann algebras in terms of 1-cohomology similar to the Delorme-Guichardet Theorem for groups. Throughout this paper N will denote a finite von Neumann algebra with a fixed normal faithful tracial state τ .

The following full text is a preprint version which may differ from the publisher's version. We study the sequential product GN01,GG02,GG05 , the operation p * q = √ pq √ p on the set of effects, [0, 1] A , of a von Neumann algebra A that represents sequential measurement of first p and then q. In GL08 Gudder andLatémolì ere give a list of axioms based on physical grounds that completely determ...

In this paper, we clarify the structure of the Stone spectrum of an arbitrary finite von Neumann algebra R of type In. The main tool for this investigation is a generalized notion of rank for projections in von Neumann algebras of this type.

We construct a real valued dimension for arbitrary modules over the algebra of operators affiliated to a finite von Neumann algebra. Moreover we determine the algebraic K0and K1-group and the Lgroups of such an algebra.

The main result of this paper is a generalization of Popa’s free independence result for subalgebras of ultraproduct II1 factors [Po95b] to the framework of ultraproduct von Neumann algebras (M, φ) where (M,φ) is a σ-finite von Neumann algebra endowed with a faithful normal state satisfying (M) ∩ M = C1. More precisely, we show that whenever P1, P2 ⊂ M ω are von Neumann subalgebras with separab...

3 We consider commuting squares of nite dimensional von Neumann algebras having the algebra of complex numbers in the lower left corner. Examples include the vertex models, the spin models (in the sense of subfactor theory) and the commuting squares associated to nite dimensional Kac algebras. To any such commuting square we associate a compact Kac algebra and we compute the corresponding subfa...