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Let $X$ be a compact metric space and let $Lambda$ be a $Z^k$ ($kge 1$) action on $X.$ We give a solution to a version of Voiculescus problem of AF-embedding: The crossed product $C(X)rtimes_{Lambda}Z^k$ can be embedded into a unital simple AF-algebra if and only if $X$ admits a strictly positive $Lambda$-invariant Borel probability measure. Let $C$ be a unital AH-algebra, let $G$ be a finitely generated abelian group and let $Lambda: Gto Aut(C)$ be a monomorphism. We show that $Crtimes_{Lambda} G$ can be embedded into a unital simple AF-algebra if and only if $C$ admits a faithful $Lambda$-invariant tracial state.
We study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. We develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to
Let $A$ be a unital AF-algebra whose Murray-von Neumann order of projections is a lattice. For any two equivalence classes $[p]$ and $[q]$ of projections we write $[p]sqsubseteq [q]$ iff for every primitive ideal $mathfrak p$ of $A$ either $p/mathfra
Let $(mathcal G, Sigma)$ be an ordered abelian group with Haar measure $mu$, let $(mathcal A, mathcal G, alpha)$ be a dynamical system and let $mathcal Artimes_{alpha} Sigma $ be the associated semicrossed product. Using Takai duality we establish a
We consider a twisted noncommutative join procedure for unital $C^*$-algebras which admit actions by a compact abelian group $G$ and its discrete abelian dual $Gamma$, so that we may investigate an analogue of Baum-Dabrowski-Hajac noncommutative Bors
Let $C$ be a general unital AH-algebra and let $A$ be a unital simple $C^*$-algebra with tracial rank at most one. Suppose that $phi, psi: Cto A$ are two unital monomorphisms. We show that $phi$ and $psi$ are approximately unitarily equivalent if and