Representations of C*-dynamical systems implemented by Cuntz families

Given a dynamical system (A,\al) where $A$ is a unital \ca-algebra and \al is a (possibly non-unital) *-endomorphism of $A$, we examine families $(\pi,\{T_i\})$ such that $\pi$ is a representation of $A$, $\{T_i\}$ is a Toeplitz-Cuntz family and a covariance relation holds. We compute a variety of non-selfadjoint operator algebras that depend on the choice of the covariance relation, along with the smallest \ca-algebra they generate, namely the \ca-envelope. We then relate each occurrence of the \ca-envelope to (a full corner of) an appropriate twisted crossed product. We provide a counterexample to show the extent of this variety. In the context of \ca-algebras, these results can be interpreted as analogues of Stacey's famous result, for non-automorphic systems and $n>1$. Our study involves also the one variable generalized crossed products of Stacey and Exel. In particular, we refine a result that appears in the pioneering paper of Exel on (what is now known as) Exel systems.Comment: 29 pages; changes in subsection 1.2; close to publicatio

Shift Endomorphisms And Compact Lie Extensions

We consider skew-products with an arbitrary compact Lie group, when the base map is a one-sided shift of finite type endowed with an equilibrium state of a Holder continuous function. First we show that the weak-mixing property of the skew-product implies exactness and exponential mixing. Then we address the problem of classification under measure-theoretic isomorphisms. We show that for a generic set of equilibrium states the isomorphism class of the skew-products corresponds essentially to the cohomology classes of the defining skewing function and the isomorphism is essentially a homeomorphism. Introduction For many problems associated with endomorphisms in Ergodic Theory it is appropriate to consider natural extensions and then to invoke, or prove, results for automorphisms. This is valid, for example, when considering certain ergodic or mixing properties or when considering certain entropy problems. However, this is not the case for, say, exactness, nor for classification theory...

Spectrally bounded operators from von Neumann algebras

Abstract. We prove that every unital spectrally bounded operator from a properly infinite von Neumann algebra onto a semisimple Banach algebra is a Jordan homomorphism

(Communicated by G. Korchmáros)

A unified construction of finite geometries associated wit