Related papers: Pointwise approximation by elementary complete con…

We consider tracial stability, which requires that tuples of elements of a C*-algebra with a trace that nearly satisfy the relation are close to tuples that actually satisfy the relation. Here both "near" and "close" are in terms of the…

Let $H$ be an infinite dimensional, reflexive, separable Hilbert space and $NA(H)$ the class of all norm-attainble operators on $H.$ In this note, we study an implicit scheme for a canonical representation of nonexpansive contractions in…

In this paper we generalize a specific quantized convexity structure of the generalized state space of a $C^*$-algebra and examine the associated extreme points. We introduce the notion of $P$-$C^*$-convex subsets, where $P$ is any positive…

Let A be a unital separable simple infinite-dimensional nuclear C*-algebra with at least one tracial state. We prove that if the trace space of A has compact finite-dimensional extreme boundary then there exist unital embeddings of matrix…

We discuss when a unital homomorphism {\phi} : C(X) \rightarrow A can be approximated by finite-dimensional homomorphisms, where X is a compact metric space and A is unital simple C*-algebra with tracial rank one. In this paper, we will…

We construct some separable infinite dimensional homogeneous Hilbertian operator spaces which generalize the row and column spaces R and C. We show that separable infinite-dimensional Hilbertian JC*-triples are completely isometric to an…

It is proved that that every nilpotent contraction in a quotient C*-algebra can be lifted to a nilpotent contraction. As a consequence we get that the universal C*-algebra generated by a nilpotent contraction is projective. This answers the…

In this paper, we prove approximate lifting results in the C$^{\ast}$-algebra and von Neumann algebra settings. In the C$^{\ast}$-algebra setting, we show that two (weakly) semiprojective unital C*-algebras, each generated by $n$…

We prove a classification theorem for purely infinte simple C*-algebras that is strong enough to show that the tensor products of two different irrational rotation algebras with the same even Cuntz algebra are isomorphic. In more detail,…

Let $a$ and $b$ be elements in the closed ball of a unital C$^*$-algebra $A$ (if $A$ is not unital we consider its natural unitization). We shall say that $a$ and $b$ are domain (respectively, range) absolutely compatible ($a\triangle_d b$,…

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 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…

Let ${\cal A}_1$ be the class of all unital separable simple $C^*$-algebras $A$ such that $A\otimes U$ has tracial rank at most one for all UHF-algebras of infinite type. It has been shown that amenable ${\cal Z}$-stable $C^*$-algebras in…

We initiate the study of pointed approximative absolute neighborhood retracts. Our motivation is to generate examples of C*-algebras that behave in unexpected ways with respect to weak semiprojectivity. We consider both weak…

We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra $\cc(M)$ of continuous functions…

Main result: If a C*-algebra is simple, $\sigma$-unital, has finitely many extremal traces, and has strict comparison of positive elements by traces, then its multiplier also has strict comparison of positive elements by traces. The same…

A $C^{*}$-algebra $A$ has ideal property if any ideal $I$ of $A$ is generated as a closed two sided ideal by the projections inside the ideal. Suppose that the limit $C^{*}$-algebra $A$ of inductive limit of direct sums of matrix algebras…

For $C^*$-algebras $A_1, A_2$ the map $(I_1,I_2)\to ker(q_{I_1}\otimes q_{I_2})$ from $Id^{\prime}(A_1)\times Id^{\prime}(A_2)$ into $Id^{\prime}(A_1\otimes_{\mathrm{min}} A_2) is a homeomorphism onto its image which is dense in the range.…

We consider derivations from the image of the canonical contraction $\theta_A$ from the Haagerup tensor product of a C*-algebra A with itself to the space of completely bounded maps on A. We show that such derivations are necessarily inner…

We say a completely positive contractive map between two C*-algebras has order zero, if it sends orthogonal elements to orthogonal elements. We prove a structure theorem for such maps. As a consequence, order zero maps are in one-to-one…