Related papers: Some quasinilpotent generators of the hyperfinite …

We present two novel results about Hilbert space operators which are nilpotent of order two. First, we prove that such operators are indestructible complex symmetric operators, in the sense that tensoring them with any operator yields a…

Let $\mathcal M$ be a separable factor. An operator $T$ in $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann algebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e.,…

In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the…

We prove that any separable II$_1$ factor $M$ admits a {\it coarse decomposition} over the hyperfinite II$_1$ factor $R$, i.e., there exists an embedding $R\hookrightarrow M$ such that $L^2M\ominus L^2R$ is a multiple of the coarse Hilbert…

We introduce "embedding dimensions" of a family of generators of a finite von Neumann algebra when the von Neumann algebra can be faithfully embedded into the ultrapower of the hyperfinite II$_1$ factor. These embedding dimensions are von…

We prove that for every semigroup of Schwarz maps on the von~Neumann algebra of all bounded linear operators on a Hilbert space which has a subinvariant faithful normal state there exists an associated semigroup of contractions on the space…

We show that a bounded quasinilpotent operator $T$ acting on an infinite dimensional Banach space has an invariant subspace if and only if there exists a rank one operator $F$ and a scalar $\alpha\in\mathbb{C}$, $\alpha\neq 0$, $\alpha\neq…

In 2005, Shen introduced a new invariant, $\mathcal G(N)$, of a diffuse von Neumann algebra $N$ with a fixed faithful trace, and he used this invariant to give a unified approach to showing that large classes of ${\mathrm{II}}_1$ factors…

To any strongly continuous orthogonal representation of $\R$ on a real Hilbert space $\CH_\R$, Hiai constructed $q$-deformed Araki-Woods von Neumann algebras for $-1< q< 1$, which are $W^{\ast}$-algebras arising from non tracial…

We prove a basic result about tensor products of a $\text{II}_1$ factor with a finite von Neumann algebra and use it to answer, affirmatively, a question asked by S. Popa about maximal injective factors.

We prove that a (bounded linear) operator acting on an infinite-dimensional, separable, complex Hilbert space can be written as a product of two quasi-nilpotent operators if and only if it is not a semi-Fredholm operator. This solves the…

For every $n\in \mathbb{N}$ we obtain a separable II$_1$ factor $M$ and a maximally abelian subalgebra $A\subset M$ such that the space of maximally amenable extensions of $A$ in $M$ is affinely identified with the $n$ dimensional…

We consider various statements that characterize the hyperfinite II$_1$ factors amongst embeddable II$_1$ factors in the non-embeddable situation. In particular, we show that "generically" a II$_1$ factor has the Jung property (which states…

This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…

Investigating a recent positive solution of a conjecture of Grunewald and O'Halloran for complex finite dimensional nilpotent Lie algebras, we are in the position to find results of existence and uniqueness for the construction of complex…

Relativizing an idea from multiplicity theory, we say that an element x of a von Neumann algebra M is n-divisible if (W*(x)' cap M) unitally contains a factor of type I_n. We decide the density of the n-divisible operators, for various n,…

Let $G$ be a locally compact group, $L(G)$ be its group von Neumann algebra equipped with the Plancherel weight $\varphi_G$. In this paper, we consider the following two questions. (1) When is the restriction of $\varphi_G$ to the…

An operator $T$ in a separable factor $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann subalgebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e., $W^*(T)'\cap\mathcal{M}=\mathbb{C}I$.…

A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…

In this paper, we prove a non-commutative version of the Weyl-von Neumann theorem for representations of unital, separable AH algebras into countably decomposable, semifinite, properly infinite, von Neumann factors, where an AH algebra…