Related papers: A nonseparable amenable operator algebra which is …

We introduce the notion of a (noncommutative) C*-Segal algebra as a Banach algebra which is a dense ideal in a C*-algebra. Several basic properties are investigated and, with the aid of the theory of multiplier modules, the structure of…

Recently, S. Carpi et al. (Comm. Math. Phys., 402:169-212, 2023) proved that every connected (i.e. haploid) Frobenius algebra in a tensor C$^*$-category is unitarizable (i.e. isomorphic to a special C$^*$-Frobenius algebra). Building on…

We construct a simple, separable, unital, and nuclear C*-algebra with weakly unperforated K_0-group which does not absorb the Jiang-Su algebra Z tensorially. As a result, we obtain a stably finite counter-example to Elliott's classification…

We present a stable uniqueness theorem for non-unital C*-algebras. Generalized tracial rank one is defined for stably projectionless simple C*-algebras. Let $A$ and $B$ be two stably projectionless separable simple amenable C*-algebras with…

Characterisations of those separable C*-algebras that have type I injective envelopes or W*-algebra injective envelopes are presented.

Three natural definitions for amenability of general Hopf C^*-algebras (all of them being generalizations of the case of locally compact groups) were given and the relations between them were studied. Moreover, amenability in the situation…

Non-commutative $L^p$-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For $p\geq 2$ they are also proved to possess a {\em sufficient} family of bounded positive sesquilinear forms…

We consider inductive systems of C*-algebras with completely positive contractive connecting maps. We define a condition, called C*-encoding, which is sufficient for the limit of the system to be completely order isomorphic to a C*-algebra…

Every separable nondegenerate C*-correspondence over a commutative C*-algebra with discrete spectrum is isomorphic to a graph correspondence.

We prove that, if a discrete group $G$ is not inner amenable, then the unit group of the ring of operators affiliated with the group von Neumann algebra of $G$ is non-amenable with respect to the topology generated by its rank metric. This…

We examine rigidity phenomena for representations of amenable operator algebras which have an ideal of compact operators. We establish that a generalized version of Kadison's conjecture on completely bounded homomorphisms holds for the…

We analyze the dichotomy amenable/paradoxical in the context of (discrete, countable, unital) semigroups and corresponding semigroup rings. We consider also F{\o}lner's type characterizations of amenability and give an example of a…

A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C*-correspondence if and only if its fundamental relation R(A) is a tree admitting a $Z^+_0$-valued continuous and coherent cocycle. For triangular limit…

Let H be a compact quantum group with faithful Haar measure and bounded counit. If H acts on a C*-algebra A, we show that A is nuclear if and only if its fixed-point subalgebra is nuclear. As a consequence H is a nuclear C*-algebra.

We study actions of countable discrete amenable groups on unital separable simple nuclear Z-absorbing C*-algebras. Under a certain assumption on tracial states, which is automatically satisfied in the case of a unique tracial state, the…

Let X be a path connected, compact metric space and let A be a unital separable simple nuclear Z-stable real rank zero C*-algebra. We classify all the unital *-embeddings (up to approximate unitary equivalence) of C(X) into A. Specifically,…

Using the natural duality between linear functionals on tensor products of C*-algebras with the trace class operators on a Hilbert space H and linear maps of the C*-algebra into B(H), we give two characterizations of separability, one…

A subset $\mathcal X$ of a C*-algebra $\mathcal A$ is called irredundant if no $A\in \mathcal X$ belongs to the C*-subalgebra of $\mathcal A$ generated by $\mathcal X\setminus \{A\}$. Separable C*-algebras cannot have uncountable…

We classify the unital embeddings of a unital separable nuclear $C^*$-algebra satisfying the universal coefficient theorem into a unital simple separable nuclear $C^*$-algebra that tensorially absorbs the Jiang--Su algebra. This gives a new…

We revisit the notion of tracial approximation for unital simple C*-algebras. We show that a unital simple separable C*-algebra A is asymptotically tracially in the class of C*-algebras with finite nuclear dimension if and only if A is…