Related papers: Completely Bounded Representations Into Von Neuman…
We show that there exists a completely bounded (c.b. in short) homomorphism $u$ from a $C^*$-algebra $C$ with the lifting property (in short LP) into a QWEP von Neumann algebra $N$ that is not strongly similar to a $*$-homomorphism, i.e.…
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…
The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra $\mathcal{O}_2$. In an effort to provide a negative solution to the KEP and motivated by the recent refutation of the Connes…
The $C^{\ast}$-algebra $\mathcal{U}_{nc}(n)$ is the universal $C^{\ast}$-algebra generated by $n^2$ generators $u_{ij}$ that make up a unitary matrix. We prove that Kirchberg's formulation of Connes' embedding problem has a positive answer…
Let $A$ be a unital $C^*$-algebra generated by some separable operator system $S$. More than a decade ago, Arveson conjectured that $S$ is hyperrigid in $A$ if all irreducible representations of $A$ are boundary representations for $S$.…
We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator…
We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of $M$ $$Id_M=vu: M{\buildrel…
We show that C*-algebras generated by irreducible representations of finitely generated nilpotent groups satisfy the universal coefficient theorem of Rosenberg and Schochet. This result combines with previous work to show that these…
We construct the first example of a $C^*$-algebra $A$ with the properties in the title. This gives a new example of non-nuclear $A$ for which there is a unique $C^*$-norm on $A \otimes A^{op}$. This example is of particular interest in…
Kirchberg's Embedding Problem (KEP) asks whether every separable C$^*$ algebra embeds into an ultrapower of the Cuntz algebra $\mathcal{O}_2$. In this paper, we use model theory to show that this conjecture is equivalent to a local…
A hereditarily atomic von Neumann algebra $A$ is a $W^*$ product of matrix algebras, regarded as the underlying function algebra of a quantum set. Projections in $A\overline{\otimes}A^{\circ}$ are interpreted as quantum binary relations on…
We use representations of operator systems as quotients to deduce various characterisations of the weak expectation property (WEP) for C?*-algebras. By Kirchberg's work on WEP, these results give new formulations of Connes' embedding…
It is proved that every separable $C^*$-algebra of real rank zero contains an AF-sub-$C^*$-algebra such that the inclusion mapping induces an isomorphism of the ideal lattices of the two $C^*$-algebras and such that every projection in a…
In this note, we derive some consequences of the von Neumann algebra uniqueness theorems developed in a previous paper (see arXiv:1207.6741v1). In particular, 1) we solvein a paper of Futamura, Kataoka, and Kishimoto, by proving that if A…
The purpose of this paper is two-fold: firstly, we give a characterization on the level of non-unital operator systems for when the zero map is a boundary representation. As a consequence, we show that a non-unital operator system arising…
Based on the analysis on the Ocneanu/Groh-Raynaud ultraproducts and the Effros-Mar\'echal topology on the space vN(H) of von Neumann algebras acting on a separable Hilbert space H, we show that for a von Neumann algebra M in vN(H), the…
We say that a contractive Hilbert space operator is universal if there is a natural surjection from its generated C*-algebra to the C*-algebra generated by any other contraction. A universal contraction may be irreducible or a direct sum of…
We prove that a discrete group $G$ is amenable iff it is strongly unitarizable in the following sense: every unitarizable representation $\pi$ on $G$ can be unitarized by an invertible chosen in the von Neumann algebra generated by the…
We prove that any irreducible $*$-representation of $\mathrm{Pol}(\mathrm{Mat}_n)_q$ can be 'lifted' to an irreducible *-representation of $\mathbb{C}[SU_{2n}]_q$, this result is then used to show the existence of the universal enveloping…
An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered.…