Related papers: On $\ell$-open $C^*$ algebras and $\ell$-closed $C…

We give a complete description of which unital graph C*-algebras are semiprojective, and use it to disprove two conjectures by Blackadar. To do so, we perform a detailed analysis of which projections are properly infinite in such…

Given a compact, metric space X, we show that the commutative C*-algebra C(X) is semiprojective if and only if X is an absolute neighborhood retract of dimension at most one. This confirms a conjecture of Blackadar. Generalizing to the…

We show that semiprojectivity of a C*-algebra is preserved when passing to C*-subalgebras of finite codimension. In particular, any pullback of two semiprojective C*-algebras over a finite-dimensional C*-algebra is again semiprojective.

We give a classification result for a certain class of $C^{*}$-algebras $\mathfrak{A}$ over a finite topological space $X$ in which there exists an open set $U$ of $X$ such that $U$ separates the finite and infinite subquotients of…

We describe the $C^*$-algebra of an $E$-unitary or strongly 0-$E$-unitary inverse semigroup as the partial crossed product of a commutative $C^*$-algebra by the maximal group image of the inverse semigroup. We give a similar result for the…

In this paper we describe all surjective isometries between open subgroups of the groups of invertible elements in unital $C^{*}$-algebras.

An open question, raised independently by several authors, asks if a closed amenable subalgebra of ${\mathcal B}({\mathcal H})$ must be similar to an amenable C*-algebra; the question remains open even for singly-generated algebras. In this…

We prolonge the list of C*-algebras for which all extensions by any stable separable C*-algebra are semi-invertible. In particular, we handle certain amalgamations, both of C*-algebras and of groups. Concerning groups we consider both…

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…

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…

We obtain partial affirmative answers to the question whether isomorphism of the unitary groups of two C*-algebras, either as topological groups or as discrete groups, implies isomorphism of the C*-algebras as real C*-algebras.

A pro-C^*-algebra is a (projective) limit of C^*-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-C^*-algebras can be seen as non-commutative k-spaces. An element of a pro-C^*-algebra…

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…

Given an arbitrary countable ordinal $\alpha $, we introduce the notion of type $I_{\alpha }$ C*-algebra and $\alpha $-subhomogeneous C*-algebra. When $\alpha =0$, these recover the notions of Fell C*-algebra and of commutative C*-algebra,…

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…

Examples of simple, separable, unital, purely infinite $C^*$--algebras are constructed, including: (1) some that are not approximately divisible; (2) those that arise as crossed products of any of a certain class of $C^*$--algebras by any…

We characterise the strictly closed left invariant C*-subalgebras of the C*-algebra C_b(G) of bounded continuous functions on a locally compact group G. On the dual side, we characterise the strictly closed invariant C*-subalgebras of the…

We prove constructive versions of various usual results related to the Gelfand duality. Namely, that the constructive Gelfand duality extend to a duality between commutative nonunital C*-algebras and locally compact completely regular…

We show that semigroup C*-algebras are groupoid C*-algebras.

Let p be a polynomial in one variable. It is shown that the universal C*-algebra of the relation p(x)=0, \|x\| \le C is semiprojective, residually finite-dimensional and has trivial extension group.