Related papers: Von Neumann equivalence and $M_d$ type approximati…

We study the relation between the linear stability of almost-symmetries and the geometry of the Banach spaces on which these transformations are defined. We show that any transformation between finite dimensional Banach spaces that…

We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth mappings by regular ones. They form a natural counterpart to…

The category of $C^*$-algebras is blessed with many different tensor products. In contrast, virtually the only tensor product ever used in the category of von Neumann algebras is the normal spatial tensor product. We propose a definition of…

In this paper, we introduce and study the persistent approximation property for quantitative K-theory of filtered C*-algebras. In the case of crossed product C*-algebras, the persistent approximation property follows from the Baum-Connes…

In this paper we study three aspects of (P(M)/~), the set of Murray-von Neumann equivalence classes of projections in a von Neumann algebra M. First we determine the topological structure that (P(M)/~) inherits from the operator topologies…

We introduce the notion of proper proximality for finite von Neumann algebras, which naturally extends the notion of proper proximality for groups. Apart from the group von Neumann algebras of properly proximal groups, we provide a number…

We will show that group exactness is a von Neumann equivalence invariant. This result generalizes the previously known fact stating that group exactness is invariant under measure equivalence and W*-equivalence.

A quantum expectation is a positive linear functional of norm one on a non-commutative probability space (i.e., a C*-algebra). For a given pair of quantum expectations $\mu$ and $\lambda$ on a non-commutative probability space $A$, we…

Suppose that $\mathcal M$ is a countably decomposable type II$_1$ von Neumann algebra and $\mathcal A$ is a separable, non-nuclear, unital C$^*$-algebra. We show that, if $\mathcal M$ has Property $\Gamma$, then the similarity degree of…

We determine when a quasi-isometry between discrete spaces is at bounded distance from a bilipschitz map. From this we prove a geometric version of the Von Neumann conjecture on amenability. We also get some examples in geometric groups…

Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…

We investigate approximation properties for $C^*$-algebras and their crossed products by actions and coactions by locally compact groups. We show that Haagerup's approximation constant is preserved for crossed products by arbitrary amenable…

We show that the space $M_d(G)$ of $M_d$-multipliers of a locally compact group $G$ is isometrically isomorphic to the Banach space of bounded functionals on the $d$-fold Haagerup tensor product of $L^1(G)$ vanishing on the kernel of the…

We establish the test which allows to show that a mean does not admit a weak-Hardy property. As a result we prove that Hardy and weak-Hardy properties are equivalent in the class of homogeneous, symmetric, repetition invariant, and Jensen…

We develop a representation theory for $\lambda$-lattices, arising as standard invariants of subfactors, and for rigid C*-tensor categories, including a definition of their universal C*-algebra. We use this to give a systematic account of…

Let $WS(X, d)$ be the class of ultrametric spaces which are weakly similar to ultrametric space $(X, d)$. The main results of the paper completely describe the ultrametric spaces $(X, d)$ for which the equality $$ \rho(x, y) = f(d(\Phi(x),…

We define a strengthening of the Haagerup-Kraus approximation property by means of the subalgebras of Herz-Schur multipliers $M_d(G)$ ($d\geq 2$) introduced by Pisier. We show that unitarisable groups satisfying this property for all $d\geq…

A theory of Galois co-objects for von Neumann bialgebras is introduced. This concept is closely related to the notion of comonoidal W*-Morita equivalence between von Neumann bialgebras, which is a Morita equivalence taking the…

We study some general properties of tracial C*-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C*-algebras. In the second part, we consider continuous bundles of tracial…

A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and…