The Hughston-Jozsa-Wootters (HJW) theorem entails that any finite ensemble compatible with a given density operator can be prepared from a fixed initial state by operations on a spacelike separated system. In this paper, we generalize the HJW theorem to the case of arbitrary measures on the state space of a von Neumann algebra with hyperfinite commutant. In doing so, we also show that every POV...

A ternary ring of operators is an “off-diagonal corner” of a C∗-algebra and the predual of a ternary ring of operators (if it exists) is of the form pR∗q for some von Neumann algebra R and projections p and q in R. In this paper, we prove that a subspace of the predual of a ternary ring of operators is completely 1-complemented if and only if it is completely isometrically isomorphic to the pre...

Many very different themes could be used for a talk such as this one, but I have chosen von Neumann algebras because they are what led me into this circle of ideas. Thus the presentation will be historical rather than logical. A von Neumann algebra M is a *~algebra of bounded operators on a Hilbert space (Jf, ( , )) which contains the identity and is closed in the weak operator topology, i.e. i...

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.