Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of Wiesbrock on certain one-parameter semigroups of endomorphisms of von Neumann algebras (specifically, Type III1 factors) that appear as lightlike translations i...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

We study asymptotic behavior of a Markov semigroup on a von-Neumann algebra by exploring a maximal von-Neumann subalgebra where the Markov semigroup is an automorphism. This enables us to prove that strong mixing is equivalent to ergodic property for continuous time Markov semigroup on a type-I von-Neumann algebra with center completely atomic. For discrete time dynamics we prove that an aperio...

The paper is devoted to local derivations on the algebra S(M, τ) of τ measurable operators affiliated with a von Neumann algebra M and a faithful normal semi-finite trace τ. We prove that every local derivation on S(M, τ) which is continuous in the measure topology, is in fact a derivation. In the particular case of type I von Neumann algebras they all are inner derivations. It is proved that f...

It will be shown that for 1 < p < 2 the Schatten p-class is isometrically isomor-phic to a subspace of the predual of a von Neumann algebra. Similar results hold for non-commutative L p (N;)-spaces deened by a semi-nite, normal, faithful trace on a von Neumann algebra N. The embeddings rely on a suitable notion of p-stable processes in the non-commutative setting.

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...

Motivated by the study of von Neumann regular skew groups as carried out by Alfaro, Ara and del Rio in [1] we investigate regular and biregular Hopf module algebras. If A is an algebra with an action by an affine Hopf algebra H, then any H-stable left ideal of A is a direct summand if and only if A is regular and the invariance functor (−) induces an equivalence of A -Mod to the Wisbauer catego...

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...