Related papers: Extensions of C*-dynamical systems to systems with…

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 study the crossed product $C^*$-algebra associated to injective endomorphisms, which turns out to be equivalent to study the crossed product by the dilated autormorphism. We prove that the dilation of the Bernoulli $p$-shift endomorphism…

Let $A$ be a unital $C^*$-algebra and $\alpha$ be an injective, unital endomorphism of $A$. A covariant representation of $(A,\alpha)$ is a pair $(\pi,T)$ consisting of a $C^*$-representation $\pi$ of $A$ on a Hilbert space $H$ and a…

We examine the semicrossed products of a semigroup action by $*$-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations…

The paper presents a construction of the crossed product of a C*-algebra by a commutative semigroup of bounded positive linear maps generated by partial isometries. In particular, it generalizes Antonevich, Bakhtin, Lebedev's crossed…

We consider Exel's new construction of a crossed product of a C*-algebra A by an endomorphism \alpha. We prove that this crossed product is universal for an appropriate family of covariant representations, and we show that it can be…

In this paper we extend the constructions of Boava and Exel to present the C*-algebra associated with an injective endomorphism of a group with finite cokernel as a partial group algebra and consequently as a partial crossed product. With…

A surjective endomorphism or, more generally, a polymorphism in the sense of \cite{SV}, of a compact abelian group $H$ induces a transformation of $L^2(H)$. We study the C*-algebra generated by this operator together with the algebra of…

For a fixed C*-algebra A, we consider all noncommutative dynamical systems that can be generated by A. More precisely, an A-dynamical system is a triple (i,B,\alpha) where $\alpha$ is a *-endomorphism of a C*-algebra B, and i: A --> B is…

The purpose of this paper is to introduce a consistent notion of universal and reduced crossed products by actions and coactions of groups on operator systems and operator spaces. In particular we shall put emphasis to reveal the full power…

We characterize when a C*-cover admits a C*-dynamical extension of dynamics on an operator algebra in terms of the boundary ideal structure for the operator algebra in its maximal representation and show that the C*-covers that admit such…

To a given multivariable C*-dynamical system $(A, \al)$ consisting of *-automorphisms, we associate a family of operator algebras $\alg(A, \al)$, which includes as specific examples the tensor algebra and the semicrossed product. It is…

Let \alpha:G --> G be an endomorphism of a discrete amenable group such that [G:\alpha(G)]<infinity. We study the structure of the C^* algebra generated by the left convolution operators acting on the left regular representation space,…

We take a new look at dilation theory for nonself-adjoint operator algebras. Among the extremal (co)extensions of a representation, there is a special property of being fully extremal. This allows a refinement of some of the classical…

Given a quasi-special endomorphism $\rho$ of a C*-algebra A with nontrivial center, we study an extension problem for automorphisms of A to a minimal cross-product B of A by $\rho$. Exploiting some aspects of the underlying generalized…

S. L. Woronowicz's theory of introducing C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators…

A $C^*$-textile dynamical system $({\cal A}, \rho,\eta,\Sigma^\rho,\Sigma^\eta, \kappa)$ connsists of a unital $C^*$-algebra ${\cal A}$, two families of endomorphisms ${\rho_\alpha}_{\alpha \in \Sigma^\rho}$ and ${\eta_a}_{a \in…

Our initial data is a transfer operator $L$ for a continuous, countable-to-one map $\varphi:\Delta \to X$ defined on an open subset of a locally compact Hausdorff space $X$. Then $L$ may be identified with a `potential', i.e. a map…

We describe simplicity of the Stacey crossed product A\times_\beta \N in terms of conditions of the endomorphism \beta. Then, we use a characterization of the graph C*-algebras C*(E) as the Stacey crossed product…

The paper presents a construction of the crossed product of a C*-algebra by a semigroup of endomorphisms generated by partial isometries.