相关论文: Voiculescu's Theorem in Properly Infinite Factors

We prove an analogue of Voiculescu's theorem: Relative bicommutant of a separable unital subalgebra $A$ of an ultraproduct of simple unital C*-algebras is equal to $A$.

In the current paper, we generalize the "compact operator" part of the Voiculescu's non-commutative Weyl-von Neumann theorem on approximate equivalence of unital $*$-homomorphisms of an commutative C$^*$ algebra $\mathcal{A}$ into a…

We prove that Voiculescu's noncommutative version of the Weyl-von Neumann theorem can be extended to all (not necessarily separable) unital, separably representable C*-algebras whose density character is strictly smaller than…

In this paper, we provide a generalized version of the Voiculescu theorem for normal operators by showing that, in a von Neumann algebra with separable pre-dual and a faithful normal semifinite tracial weight $\tau$, a normal operator is an…

A famous question of Halmos asks whether every operator on a separable infinite-dimensional Hilbert space is a norm limit of reducible operators. In [30], Voiculescu gave this problem an affirmative answer by his remarkable non-commutative…

We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue of the Bercovici-Pata…

In 1976, D. Voiculescu proved that every separable unital sub-C*-algebra of the Calkin algebra is equal to its (relative) bicommutant. In his minicourse (see reference), G. Pedersen asked in 1988 if Voiculescu's theorem can be extended to a…

We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility when having approximate identities at hand, and, on the other side, it is a direct…

Aided by the tools and outlook provided by modern classification theory, we take a new look at the Brown-Voiculescu entropy of endomorphisms of nuclear C*-algebras. In particular, we introduce `coloured' versions of noncommutative…

We present the analytic foundation of a unified B-D-F extension functor $\operatorname{Ext}_\tau$ on the category of noncommutative smooth algebras, for any Fr\'echet operator ideal $\Cal K_\tau$. Combining the techniques devised by Arveson…

The main result of this paper is a characterization of properly infinite injective von Neumann algebras and of nuclear C*-algebras by using a uniqueness theorem, based on generalizations of Voiculescu's famous Weyl-von Neumann theorem.

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,…

Suppose B is an ultraproduct of finite dimensional C^\ast-algebras. We consider mapping and injectability properties for separable C^\ast-algebras into B. In the case of approximately finite C^\ast-algebras, we obtain a classification of…

We prove a technical result, showing that the existence of a closable unbounded dual system in the sense of Voiculescu is equivalent to the finiteness of free Fisher information. This approach allows one to give a purely operator-algebraic…

Let $A$ be a separable, unital and exact $C^*$-algebra satisfying the universal coefficient theorem. We prove uniqueness theorems up to unitary conjugacy for unital, full and nuclear maps from $A$ into ultraproducts of finite von Neumann…

The "similarity" degree of a unital operator algebra $A$ was defined and studied in two recent papers of ours, where in particular we showed that it coincides with the "length" of an operator algebra. This paper brings several complements:…

We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…

We find an elementary proof for Voiculescu's theorem on the polar decomposition of circular variables.

In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result…

The DT-operators are introduced, one for every pair (\mu,c) consisting of a compactly supported Borel probability measure \mu on the complex plane and a constant c>0. These are operators on Hilbert space that are defined as limits in…