Related papers: Some consequences of von Neumann algebra uniquenes…

Let M be a factor of type III with separable predual and with normal states phi_1,...,phi_k, omega with omega faithful. Let A be a finite dimensional C*-subalgebra of M. Then it is shown that there is a unitary operator u in M such that…

We consider the boundary-path groupoids of topological higher-rank graphs. We show that the all such groupoids are topologically amenable. We deduce that the C*-algebras of topological higher-rank graphs are nuclear and prove versions of…

We prove a non-commutative version of the Hilbert's 17th problem, giving a characterization of the class of non-commutative polynomials in n-undeterminates that have positive trace when evaluated in n-selfadjoint elements in arbitrary II1…

We prove that every positive trace on a countably generated *-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial *-algebra can be embedded into a metric…

In this note we include two remarks about bounded ($\underline{not}$ necessarily contractive) linear projections on a von Neumann-algebra. We show that if $M$ is a von Neumann-subalgebra of $B(H)$ which is complemented in B(H) and…

We show that if G is a discrete group which does not have the Haagerup property but does have an unbounded cocycle into a C_0 representation and if G acts on a finite von Neumann algebra B such that the inclusion B \subset (B \rtimes G) has…

Let $a,b$ be elements in a unital C$^*$-algebra with $0\leq a,b\leq 1$. The element $a$ is absolutely compatible with $b$ if $$\vert a - b \vert + \vert 1 - a - b \vert = 1.$$ In this note we find some technical characterizations of…

We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…

Jolissaint and Stalder introduced definitions of mixing and weak mixing for von Neumann subalgebras of finite von Neumann algebras. In this note, we study various algebraic and analytical properties of subalgebras with these mixing…

For any unital separable simple infinite-dimensional nuclear C*-algebra with finitely many extremal traces, we prove that Z-absorption, strict comparison, and property (SI) are equivalent. We also show that any unital separable simple…

We develop a new approach to non-Hausdorff \'etale groupoids and their algebras based on Timmermann's construction of Hausdorff covers. As an application, we completely characterise when singular ideals vanish in Steinberg algebras over…

The literature contains interesting examples of inclusions of simple C$^*$-algebras with the property that all intermediate C$^*$-algebras likewise are simple. In this article we take up a systematic study of such inclusions, which we refer…

Say that a separable, unital C*-algebra D is strongly self-absorbing if there exists an isomorphism $\phi: D \to D \otimes D$ such that $\phi$ and $id_D \otimes 1_D$ are approximately unitarily equivalent $*$-homomorphisms. We study this…

For unital $C^*$-algebras $A$ and $B$, we completely characterize the isometric ($*$-) automorphisms of their Banach space projective tensor product $A\otimes^\gamma B$. This leads to the characterization of inner and outer isometric…

The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra $\cal O_2$. Motivated by the recent refutation of the Connes Embedding Problem using the quantum complexity result MIP*=RE, we…

We prove that every AF-algebra is isomorphic to a crossed product of a commutative AF-algebra by a partial automorphism. The case of UHF-algebras is treated in detail.

We prove that the approximately inner automorphism group of a separable strongly stable von Neumann algebra is contractible in the u-topology. Thus the automorphism group of the hyperfinite type III_1 factor is contractible.

We consider the analogues of the Horn inequalities in finite von Neumann algebras, which concern the possible spectral distributions of sums $a+b$ of self--adjoint elements $a$ and $b$ in a finite von Neumann algebra. It is an open question…

For any locally compact group $G$, we show the existence and uniqueness up to quasi-equivalence of a unitary $C_0$-representation $\pi_0$ of $G$ such that all coefficient functions of $C_0$-representations of $G$ are coefficient functions…

A classic theorem of T. Ando characterises operators that have numerical radius at most one as operators that admit a certain positive 2x2 operator matrix completion. In this paper we consider variants of Ando's theorem, in which the…