Related papers: Relative weak injectivity of operator system pairs

We consider the properties weak cancellation, K_1-surjectivity, good index theory, and K_1-injectivity for the class of extremally rich C*-algebras, and for the smaller class of isometrically rich C*-algebras. We establish all four…

It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C$^*$-algebra. This implies that the weakly almost periodic functionals on $M(G)$, the measure…

We will study some modifications to the notion of an exact C*-algebra by replacing the minimal tensor product with the reduced free product. First we will demonstrate how the reduced free product of a short exact sequence of C*-algebras…

The study of open quantum systems relies on the notion of unital completely positive semigroups on $C^*$-algebras representing physical systems. The natural generalisation would be to consider the unital completely positive semigroups on…

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…

In this paper we give a formula for the $K$-theory of the $C^*$-algebra of a weakly left-resolving labelled space. This is done by realising the $C^*$-algebra of a weakly left-resolving labelled space as the Cuntz-Pimsner algebra of a…

Let $S$ be a concrete operator system represented on some Hilbert space $H$. A $C^*$-support of $S$ is the $C^*$-algebra generated (via the Choi--Effros product) by $S$ inside an injective operator system acting on $H$. By leveraging…

In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a…

We prove that, under certain conditions, uniform weak mixing (to zero) of the bounded sequences in Banach space implies uniform weak mixing of its tensor product. Moreover, we prove that ergodicity of tensor product of the sequences in…

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…

Recently Blecher and Kashyap have generalized the notion of W* modules over von Neumann algebras to the setting where the operator algebras are \sigma- weakly closed algebras of operators on a Hilbert space. They call these modules weak*…

We reformed the tensor product theory of vertex operator algebras developed by Huang and Lepowsky so that we could apply it to all vertex operator algebras satisfying C_2-cofiniteness. We also showed that the tensor product theory develops…

We establish the dual equivalence of the category of (potentially nonunital) operator systems and the category of pointed compact nc (noncommutative) convex sets, extending a result of Davidson and the first author. We then apply this dual…

We give an introduction to the theory of weak Hopf algebras proposed recently as a coassociative alternative of weak quasi-Hopf algebras. We follow an axiomatic approach keeping as close as possible to the "classical" theory of Hopf…

We introduce algebraic dynamical systems, which consist of an action of a right LCM semigroup by injective endomorphisms of a group. To each algebraic dynamical system we associate a C*-algebra and describe it as a semigroup C*-algebra. As…

We characterize weak* closed unital vector spaces of operators on a Hilbert space $H$. More precisely, we first show that an operator system, which is the dual of an operator space, can be represented completely isometrically and weak*…

Using the recently developed notion of a Herz--Schur multiplier of a C*-dynamical system we introduce weak amenability of C*- and W*-dynamical systems. As a special case we recover Haagerup's characterisation of weak amenability of a…

In this article we study analogues of the weak expectation property of discrete group C*-algebras and their crossed products, in the discrete quantum group setting, i.e., discrete quantum group C*-algebras and crossed products of…

We give an order-theoretic characterization of the essential image of the forgetful functor from the category of real/complex unital C*-algebras to the category of real/complex unital operator systems. It is based on the characterization of…

Following up on previous work, we prove a number of results for C*-algebras with the weak ideal property or topological dimension zero, and some results for C*-algebras with related properties. Some of the more important results include:…