Related papers: Some functorial properties of Schatten classes
In this paper we study spectral properties of non-selfadjoint operators with the discrete spectrum. The main challenge is to represent a complete description of belonging to the Schatten class through the properties of the Hermitian real…
We show that there is a functor from the category of positive admissible ternary rings to the category of $*$-algebras, which induces an isomorphism of partially ordered sets between the families of $C^*$-norms on the ternary ring and its…
In this paper, we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras,…
In recent years the theory of dendroidal sets has emerged as an important framework for higher algebra. In this article we introduce the concept of a $C^*$-algebraic drawing of a dendroidal set. It depicts a dendroidal set as an object in…
We introduce notions of the Rohlin property and the approximate representability for inclusions of unital $C^*$-algebras. We investigate a dual relation between the Rohlin property and the approximate representability. We prove that a…
Generalizing work by Pinzari and Roberts, we characterize actions of a compact quantum group G on C*-algebras in terms of what we call weak unitary tensor functors from Rep G into categories of C*-correspondences. We discuss the relation of…
We characterize exotic C*-algebras of twisted, principal \'etale groupoids, together with the abelian subalgebra associated to the unit space, as precisely being the inclusions "$A\subseteq B$" of C*-algebras in which $A$ is abelian,…
We classify unital monomorphisms into certain simple Z-stable C^*-algebras up to approximate unitary equivalence. The domain algebra C is allowed to be any unital separable commutative C^*-algebra, or any unital simple separable nuclear…
A left ideal of any $C^*$-algebra is an example of an operator algebra with a right contractive approximate identity (r.c.a.i.). Indeed left ideals in $C^*$-algebras may be characterized as the class of such operator algebras, which happen…
The aim of this lecture is to present the concept of C-algebra and to illustrate its applications in two contexts: the study of reflection groups and their folding on the one hand, the structure of rational conformal field theories on the…
We define a Riesz type interpolation property for the Cuntz semigroup of a $C^*$-algebra and prove it is satisfied by the Cuntz semigroup of every $C^*$-algebra with the ideal property. Related to this, we obtain two characterizations of…
We give the first examples of (non-amenable group) amenable actions on stably finite simple C*-algebras. More precisely, we give such actions for any countable group in an explicit way. The main ingredients of our construction are the full…
We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility…
A partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space $C^*$-algebras are isomorphic. An improved characterization of simplicity for labelled space $C^*$-algebras…
C*-algebras are widely used in mathematical physics to represent the observables of physical systems, and are sometimes taken as the starting point for rigorous formulations of quantum mechanics and classical statistical mechanics.…
Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C(X)-algebra to any precosheaf of C*-algebras A defined over K. Afterwards we consider the representation theory and the Kasparov…
We characterize the ideal of continuous-trace elements in a separable transformation-group $C^{*}$-algebra $C_0(X)\times G$. In addition, we identify the largest Fell ideal, the largest liminal ideal and the largest postliminal ideal.
This is a graduate-level introduction to C*-algebras, Hilbert C*-modules, vector bundles, and induced representations of groups and C*-algebras, with applications to quantization theory, phase space localization, and configuration space…
Exotic group $C^*$-algebras are $C^*$-algebras that lie between the universal and the reduced group $C^*$-algebra of a locally compact group. We consider simple Lie groups $G$ with real rank one and investigate their exotic group…
A class of C*-algebras is described for which the homomorphism from $C_0(0,1]$ to the algebra may be classified by means of the Cuntz semigroup functor. Examples are given of algebras--simple and non-simple--for which this classification…