Related papers: Ideal structure of crossed products by endomorphis…

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…

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…

Starting from an arbitrary endomorphism $\alpha$ of a unital C*-algebra $A$ we construct a bigger C*-algebra $B$ and extend $\alpha$ onto $B$ in such a way that the extended endomorphism $\alpha$ has a unital kernel and a hereditary range,…

Starting from an arbitrary endomorphism \delta of a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,\delta) but also on the choice of an ideal J…

Starting from an arbitrary endomorphism \alpha of a unital C*-algebra A we construct a crossed product. It is shown that the natural construction depends not only on the C*-dynamical system (A,\alpha) but also on the choice of an ideal…

We consider a family of dynamical systems (A,alpha,L) in which alpha is an endomorphism of a C*-algebra A and L is a transfer operator for \alpha. We extend Exel's construction of a crossed product to cover non-unital algebras A, and show…

Let $\mathcal{C}$ be a C*-algebra and $\alpha:\mathcal{C} \rightarrow \mathcal{C}$ a unital *-endomorphism. There is a natural way to construct operator algebras which are called semicrossed products, using a convolution induced by the…

We introduce crossed products of a $C^*$-algebra $A$ by a completely positive map $\varrho:A\to A$ relative to an ideal in $A$. They generalize various crossed products by endomorphisms when $\varrho$ is multiplicative. When $A$ is…

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…

Given a spectral triple on a $C^*$-algebra $\mathcal A$ together with a unital injective endomorphism $\alpha$, the problem of defining a suitable crossed product $C^*$-algebra endowed with a spectral triple is addressed. The proposed…

We use a characterization of the graph C*-algebras C*(E) as the Stacey crossed product C*(E)^\gamma \times_{\beta_E} N, to study its ideal properties in terms of the (non-classical) C*-dynamical system (C*(E)^\gamma, \beta_E)

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…

Let $X$ be an infinite compact metric space with finite covering dimension and let $\alpha, \beta : X\to X$ be two minimal homeomorphisms. We prove that the crossed product $C^*$-algebras $C(X)\rtimes_\alpha\Z$ and $C(X)\rtimes_\belta\Z$…

Let $A\subseteq B$ be a $C^*$-inclusion. We give efficient conditions under which $A$ separates ideals in $B$, and $B$ is purely infinite if every positive element in $A$ is properly infinite in $B$. We specialise to the case when $B$ is a…

Let $(\A, \alpha)$ and $(\B, \beta)$ be C*-dynamical systems and assume that $\A$ is a separable simple C*-algebra and that $\alpha$ and $\beta$ are *-automorphisms. Then the semicrossed products $\A \times_{\alpha} \bbZ^{+}$ and $\B…

A construction of reversible extensions of dynamical systems which applies to arbitrary mappings (not necessarily with open range) is presented. It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to…

Let $(A, \alpha)$ and $(B, \beta)$ be C*-dynamical systems where $\alpha$ and $\beta$ are arbitrary *-endomorphisms. When $\alpha$ is injective or surjective, we show that the semicrossed products $A \times_\alpha \mathbb{Z}$ and $B…

Given a weak Kac system with duality $(\mathcal{H},V,U)$ arising from regular $\mathrm{C}^{*}$-algebraic locally compact quantum group $(\mathcal{G},\Delta)$, a $\mathrm{C}^{*}$-algebra $A$, and a sufficiently well-behaved coaction…

Starting from a discrete $C^*$-dynamical system $(\mathfrak{A}, \theta, \omega_o)$, we define and study most of the main ergodic properties of the crossed product $C^*$-dynamical system $(\mathfrak{A}\rtimes_\alpha\mathbb{Z}, \Phi_{\theta,…

Given a closed ideal I in a C*-algebra A, an ideal J (not necessarily closed) in I, a *-homomorphism \al:A --> M(I) and a map L:J --> A with some properties, based on [3] and [9] we define a C*-algebra O(A,\al,L) which we call the "Crossed…