Related papers: Strict essential extensions of C*-algebras and Hil…

In Rev. Math. Phys. 4 (1997) 785 we study Hilbert-C* systems {F,G} where the fixed point algebra A has nontrivial center Z and where A'\cap F=Z is satisfied. The corresponding category of all canonical endomorphisms of A contains…

In the paper we describe the C*-algebras of noncommutative spherical tight frames over some C*-algebras and then apply to study the noncommutative version of the universal classifying space.

In this paper, we investigate some characterizations of dual continuous frames and give some results about them. Also, we refer to the method of constructing a family of duals through a fixed dual and show there exists a one-to-one…

A ring $R$ with center $C$ is said to be centrally essential if the module $R_C$ is an essential extension of the module $C_C$. In this paper, we study properties of ideals of centrally essential rings, centrally essential quaternion…

We investigate the set of maximally mixed states of a C*-algebra, extending previous work by Alberti on von Neumann algebras. We show that, unlike for von Neumann algebras, the set of maximally mixed states of a C*-algebra may fail to be…

Given a correspondence X over a C*-algebra A, we construct a C*-algebra and a Hilbert C*-bimodule over it whose crossed product is isomorphic to the augmented Cuntz-Pimsner C*-algebra of X. This construction enables us to establish a…

We study the theory of a Hilbert space H as a module for a unital C*-algebra A from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are…

Motivated by the theory of tensor algebras and multivariable C*-dynamics, we revisit two fundamental techniques in the theory of C*-correspondences, the "addition of a tail" to a non-injective C*-correspondence and the dilation of an…

The paper is devoted to continuous frames and Riesz bases in Hilbert C*-modules. we define a continuous Riesz basis for Hilbert C*-modules and give some results about them.

Due to the corresponding fact concerning Hilbert spaces, it is natural to ask if the linearity and the orthogonality structure of a Hilbert $C^*$-module determine its $C^*$-algebra-valued inner product. We verify this in the case when the…

A class of CW-complexes, called self-similar complexes, is introduced, together with C*-algebras A_j of operators, endowed with a finite trace, acting on square-summable cellular j-chains. Since the Laplacian Delta_j belongs to A_j,…

Hilbert modules over a $C^*$-category were first defined by Mitchener, who also proved that they form a $C^*$-category. An Eilenberg-Watts theorem for Hilbert modules over $C^*$-algebras was proved by Blecher. We follow a similar path to…

A C*-algebra $A$ is C*-reflexive if any countably generated Hilbert C*-module $M$ over $A$ is C*-reflexive, i.e. the second dual module $M''$ coincides with $M$. We show that a commutative C*-algebra $A$ is C*-reflexive if and only if for…

We give an alternative construction of the essential $C^*$-algebra of an \'etale groupoid, along with an ``amenability'' notion for such groupoids that is implied by the nuclearity of this essential $C^*$-algebra. In order to do this we…

This paper deals mainly with some aspects of the adjointable operators on Hilbert $C^*$-modules. A new tool called the generalized polar decomposition for each adjointable operator is introduced and clarified. As an application, the general…

This paper is about the reduced group C*-algebras of real reductive groups, and about Hilbert C*-modules over these C*-algebras. We shall do three things. First we shall apply theorems from the tempered representation theory of reductive…

We consider operators on $L^2$ spaces that expand the support of vectors in a manner controlled by some constraint function. The primary objects of study are $\mathrm C^*$-algebras that arise from suitable families of constraints, which we…

This paper studies direct limits of full upper triangular matrix algebras with embeddings which are not *-extendible. A representation of the limit algebra is found so that the generated C*-algebra is the C*-envelope. Some examples are…

Various notions of joint majorization are examined in continuous matrix algebras. The relative strengths of these notions are established via proofs and examples. In addition, the closed convex hulls of joint unitary orbits are completely…

We investigate the closed convex hull of unitary orbits of selfadjoint elements in arbitrary unital C*-algebras. Using a notion of majorization against unbounded traces, a characterization of these closed convex hulls is obtained.…