Related papers: Dilation theory, commutant lifting and semicrossed…

We develop elements of a general dilation theory for operator-valued measures and bounded linear maps between operator algebras that are not necessarily completely-bounded. We prove our main results by extending and generalizing some known…

We study partial actions of exact discrete groups on C*-algebras. We show that the partial crossed product of a commutative C*-algebra by an exact discrete group is nuclear whenever the full and reduced partial crossed products coincide.…

We show that for a class of operator algebras satisfying a natural condition the $C^*$-envelope of the universal free product of operator algebras $A_i$ is given by the free product of the $C^*$-envelopes of the $A_i$. We apply this theorem…

We give a new definition for the crossed-product of a C*-algebra A by a *-endomorphism \alpha, which depends not only on the pair (A,\alpha) but also on the choice of a transfer operator (defined in the paper). With this we generalize some…

We use the boundary-path space of a finitely-aligned k-graph \Lambda to construct a compactly-aligned product system X, and we show that the graph algebra C^*(\Lambda) is isomorphic to the Cuntz-Nica-Pimsner algebra NO(X). In this setting,…

We study C*-algebra endomorphims which are special in a weaker sense w.r.t. the notion introduced by Doplicher and Roberts. We assign to such endomorphisms a geometrical invariant, representing a cohomological obstruction for them to be…

We introduce the notion of $Q$-commuting operators which is a generalization of commuting operators. We prove a generalized version of commutant lifting theorem and Ando's dilation theorem in the context of $Q$-commuting operators.

In a recent paper, Pardo and the first named author introduced a class of C*-algebras which which are constructed from an action of a group on a graph. This class was shown to include many C*-algebras of interest, including all Kirchberg…

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that the endomorphism itself becomes induced by the bimodule of continuous sections of a vector bundle. Some motivating examples for such a construction…

Consider a projective limit G of finite groups G_n. Fix a compatible family \delta^n of coactions of the G_n on a C*-algebra A. From this data we obtain a coaction \delta of G on A. We show that the coaction crossed product of A by \delta…

For a number of properties of C*-algebras, including real rank zero, stable rank one, pure infiniteness, residual hereditary infiniteness, the combination of pure infiniteness and the ideal property, the property of being an AT algebra with…

Let P be a left LCM semigroup, and $\alpha$ an action of $P$ by endomorphisms of a $C^{*}$-algebra $A$. We study a semigroup crossed product $C^{*}$-algebra in which the action $\alpha$ is implemented by partial isometries. This crossed…

We introduce what we call "alternative twisted tensor products" for not necessarily associative algebras, as a common generalization of several different constructions: the Cayley-Dickson process, the Clifford process and the twisted tensor…

We associate a pro-C*-algebra to a pro-C*-correspondence and show that this construction generalizes the construction of crossed products by Hilbert pro-C*-bimodules and the construction of pro-C*-crossed products by strong bounded…

A collection of partial isometries whose range and initial projections satisfy a specified set of conditions often gives rise to a partial representation of a group. The C*-algebra generated by the partial isometries is thus a quotient of…

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 show that every interaction group extending an action of an Ore semigroup by injective unital endomorphisms of a C*-algebra, admits a dilation to an action of the corresponding enveloping group on another unital C*-algebra, of which the…

The weak operator topology closed operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive operator algebra, in the…

The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…

In the first part of the paper, we develop a theory of crossed products of a $C^*$-algebra $A$ by an arbitrary (not necessarily extendible) endomorphism $\alpha:A\to A$. We consider relative crossed products $C^*(A,\alpha;J)$ where $J$ is…