Related papers: Majorization in C*-algebras

In analogy with the C*-algebra theory, we study variants appropriate to nonselfadjoint algebras of nuclearity, the local lifting property, exactness, and the weak expectation property. In addition, we study the relationships between these…

We study variants of the Dixmier property that apply to elements of a unital C*-algebra, rather than to the C*-algebra itself. By a Dixmier element in a C*-algebra we understand one that can be averaged into a central element by means of a…

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*-algebras as…

The problem of inner vs outer conjugacy of subalgebras of certain graph C*-algebras is investigated. For a large class of finite graphs E, we show that whenever $\alpha$ is a vertex-fixing quasi-free automorphism of the corresponding graph…

We investigate relations on elements in C*-algebras, including *-polynomial relations, order relations and all relations that correspond to universal C*-algebras. We call these C*-relations and define them axiomatically. Within these are…

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…

We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to connect `nonselfadjoint operator algebra' with the…

Let $H$ be a separable Hilbert space with a fixed orthonormal basis. Let $\mathbb B^{(k)}(H)$ denote the set of operators, whose matrices have no more than $k$ non-zero entries in each line and in each column. The closure of the union (over…

The main result concerns a sigma-unital C*-algebra A, a strongly lower semicontinuous element h of A**, the enveloping von Neumann algebra, and the set of self-adjoint elements a of A such that a \le h - delta 1 for some delta > 0, where 1…

We study $C^*$-algebras arising from $C^*$-correspondences, which was introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our $C^*$-algebras to be nuclear, exact, or satisfy the Universal…

Spielberg's construction of C*-algebras from left cancellative small categories is a common generalization for most C*-algebras one would consider to come from ``combinatorial data,'' including graph and $k$-graph C*-algebras, Li's…

We study the validity of the Blackadar-Kirchberg conjecture for extensions of separable, nuclear, quasidiagonal $C^*$-algebras that satisfy the UCT. More specifically, we show that the conjecture for the extension has an affirmative answer…

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…

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…

We prove that the $L_1$-norms associated with a positive element $a$ of a unital C*-algebra are equivalent to the norm of C*-algebra if and only if $a$ is invertible.

Nuclear $C^*$-algebras having a system of completely positive approximations formed with convex combinations of a uniformly bounded number of order zero summands are shown to be approximately finite dimensional.

This dissertation concerns the classification of groupoid and higher-rank graph C*-algebras and has two main components. Firstly, for a groupoid it is shown that the notions of strength of convergence in the orbit space and…

We introduce a notion of a uniform structure on the set of all representations of a given separable, not necessarilly commutative $C^*$-algebra $\mathfrak{A}$ by introducing a suitable family of metrics on the set of representations of…

We introduce the concept of finitely coloured equivalence for unital *-homomorphisms between C*-algebras, for which unitary equivalence is the 1-coloured case. We use this notion to classify *-homomorphisms from separable, unital, nuclear…

We study uniform perturbations of intermediate C*-subalgebras of inclusions of simple C*-algebras. If a unital simple C*-algebra has a simple C*-subalgebra of finite index, then sufficiently close simple intermediate C*-subalgebras are…