相关论文: Random Operators and Crossed Products

Spectral theory and functional calculus for unbounded self-adjoint operators on a Hilbert space are usually treated through von Neumann's Cayley transform. Based on ideas of Woronowicz, we redevelop this theory from the point of view of…

We study quantum bipartite systems in a random pure state, where von Neumann entropy is considered as a measure of the entanglement. Expressions of the first and second exact cumulants of von Neumann entropy, relevant respectively to the…

We introduce a way of regarding Hilbert von Neumann modules as spaces of operators between Hilbert space, not unlike [Skei], but in an apparently much simpler manner and involving far less machinery. We verify that our definition is…

We examine crossed product C*-algebras associated with non-minimal free actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable…

We will extend earlier transference results of Neuwirth and Ricard from the context of noncommutative $L_p$-spaces associated with amenable groups to that of noncommutative $L_p$-spaces over crossed products of amenable and trace-preserving…

Let $A$ and $B$ be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.

In this article, we discuss some applications of the well-known Douglas factorization lemma in the context of von Neumann algebras. Let $\mathcal{B}(\mathscr{H})$ denote the set of bounded operators on a complex Hilbert space $\mathscr{H}$,…

Starting from an arbitrary endomorphism \alpha of a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,\alpha) but also on the choice of an ideal…

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that it becomes induced by a Hilbert C(X)-bimodule. Furthermore we introduce the notion of C(X)-category, and discuss relationships with crossed products…

We extend from the hyperfinite setting to general von Neumann algebras Mosonyi and Ogawa's (2015) and Mosonyi and Hiai's (2023) results showing the operational interpretation of sandwiched relative R\'enyi entropy in the strong converse of…

Let $\mathcal{C}$ be a C*-algebra and $\alpha:\mathcal{C} \rightarrow \mathcal{C}$ a unital *-endomorphism. There is a natural way to construct operator algebras which are called semicrossed products, using a convolution induced by the…

Several techniques together with some partial answers are given to the questions of factoriality, type classification and fullness for amalgamated free product von Neumann algebras.

I show that an analog of the crossed product construction that takes type $III_{1}$ algebras to type $II$ algebras exists also in the type $I$ case. This is particularly natural when the local algebra is a non-trivial direct sum of type $I$…

We discuss the cyclic homology of crossed product algebras from the Cuntz-Quillen point of view. The periodic cyclic homology of a crossed product algebra $A\rtimes G$ is described in terms of the $G$-action on periodic cyclic bicomplexes…

In the eighties, A. Connes and E. J. Woods made a connection between hyperfinite von Neumann algebras and Poisson boundaries of time dependent random walks. The present paper explains this connection and gives a detailed proof of two…

Let $\mathfrak{M}$ be a semifinite von Neumann algebra on a Hilbert space equipped with a faithful normal semifinite trace $\tau$. A closed densely defined operator $x$ affiliated with $\mathfrak{M}$ is called $\tau$-measurable if there…

All physical observations are made relative to a reference frame, which is a system in its own right. If the system of interest admits a group symmetry, the reference frame observing it must transform commensurately under the group to…

Let $A$ and $B$ be two densely defined unbounded closeable operators in a Hilbert space such that their unbounded operator products $AB$ and $BA$ are also densely defined. Then all four operators possess adjoints and we obtain new inclusion…

Semicrossed product algebras have been used to study dynamical systems since their introduction by Arveson in 1967. In this survey article, we discuss the history and some recent work, focussing on the conjugacy problem, dilation theory and…

In this work we study Schatten-von Neumann classes of tensor products of invariant operators on Hilbert spaces. In the first part we first deduce some spectral properties for tensors of anharmonic oscillators thanks to the knowledge on…