Related papers: A Note on Approximate Liftings

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…

Approximate morphisms have seen significant study across many areas of mathematics, for instance, in the theory of Absolute (Neighborhood) Retracts in topology, or of almost-commuting unitary matrices in analysis. This paper initiates study…

We prove a complete analog of the Borsuk Homotopy Extension Theorem for arbitrary semiprojective C*-algebras. We also obtain some other results about semiprojective C*-algebras: a partial lifting theorem with specified quotient, a lifting…

Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, with $K$ a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive…

By the Gelfand-Naimark theorem, any C*-algebra is isometrically isomorphic to a *-algebra of bounded operators on a Hilbert space which is closed with respect to the topology induced by the operator norm. Hence, the C*-algebras furnish an…

We study lifting properties for full product C*-algebras with amalgamation over ${\mathbb C}1$ and give new proofs for some results of Kirchberg and Pisier. We extend the result of Choi on the quasidiagonality of $C^*({\mathbb F}_n)$,…

We generalize some basic C*-algebra and von Neumann algebra theory on hereditary C*-subalgebras and projections. In particular, we extend Murray-von Neumann equivalence from projections to *-annihilators and show that several of its…

It is proved that every separable $C^*$-algebra of real rank zero contains an AF-sub-$C^*$-algebra such that the inclusion mapping induces an isomorphism of the ideal lattices of the two $C^*$-algebras and such that every projection in a…

In this paper, for a C*-Algebra A with M = M(A) an AW*-algebra, or equivalently, for an essential, norm-closed, two-sided ideal A of an AW*-algebra M, we investigate the strict approximability of the elements of M from commutative C*-…

We characterize the lifting property (LP) of a separable $C^*$-algebra $A$ by a property of its maximal tensor product with other $C^*$-algebras, namely we prove that $A$ has the LP if and only if for any family $(\{D_i\mid i\in I\}$ of…

Let $A$ be a separable amenable $C^*$-algebra and $B$ a non-unital and $\sigma$-unital simple $C^*$-algebra with continuous scale ($B$ need not be stable). We classify, up to unitary equivalence, all essential extensions of the form $0…

Let A be a C*-algebra and A** its enveloping von Neumann algebra. C. Akemann suggested a kind of non-commutative topology in which certain projections in A** play the role of open sets. The adjectives "open", "closed", "compact", and…

We extend work of the first author concering relative double commutants and approximate double commutants of unital subalgebras of unital C*-algebras, including metric versions involving distance estimates. We prove metric results for AH…

We prove that every positive trace on a countably generated *-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial *-algebra can be embedded into a metric…

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.

We establish the tracial stability of a certain class of graph products of C*-algebras. This result involves the development of the "pincushion class" of finite graphs. We then apply this result in two ways. The first application yields a…

A $C^*$-algebra $A$ is said to have the homotopy lifting property if for all $C^*$-algebras $B$ and $E$, for every surjective $^*$-homomorphism $\pi \colon E \rightarrow B$ and for every $^*$-homomorphism $\phi \colon A \rightarrow E$, any…

In the current paper, we generalize the "compact operator" part of the Voiculescu's non-commutative Weyl-von Neumann theorem on approximate equivalence of unital $*$-homomorphisms of an commutative C$^*$ algebra $\mathcal{A}$ into a…

We consider various lifting problems for C*-algebras. As an application of our results we show that any commuting family of order zero maps from matrices to a von Neumann central sequence algebra can be lifted to a commuting family of order…

We show that there exists a completely bounded (c.b. in short) homomorphism $u$ from a $C^*$-algebra $C$ with the lifting property (in short LP) into a QWEP von Neumann algebra $N$ that is not strongly similar to a $*$-homomorphism, i.e.…