Related papers: Dimension and dynamical entropy for metrized C*-al…

Suppose f is a C^{1+\epsilon} surface diffeomorphism with positive topological entropy. For every positive \delta strictly smaller than the topological entropy of f we construct an invariant Borel set E such that (a) f|E has a countable…

Using free probability constructions involving Cuntz-Pimsner C*-algebras we show that the topological entropy of the free product of two automorphisms is equal to the maximum of the individual entropies. As applications we show that general…

Certain classes of automorphisms of recued amalgamated free products of C*-algebras are shown to have Brown-Voiculescu topological entropy zero. Also, for automorphisms of exact C*-algebras, the Connes-Narnhofer-Thirring entropy is shown to…

Let a compact Lie group act ergodically on a unital $C^*$-algebra $A$. We consider several ways of using this structure to define metrics on the state space of $A$. These ways involve length functions, norms on the Lie algebra, and Dirac…

We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative…

In this paper an automorphism of a unital C*-algebra is said to be /locally inner/ if on any element it agrees with some inner automorphism. We make a fairly complete study of local innerness in von Neumann algebras, incorporating…

For $p\geq 2$, the $p$-adic ring $C^*$-algebra $\mathcal{Q}_p$ is the universal $C^*$-algebra generated by a unitary $U$ and an isometry $S_p$ such that $S_pU=U^pS_p$ and $\sum_{l=0}^{p-1}U^lS_pS_p^*U^{-l}=1$. For any $k$ coprime with $p$…

We show that certain C*-algebras which have been studied among others by Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving transformation of a measure space and/or to a covering map of a compact space are…

Building off work of Farenick and Rahaman, we extend the definition of the density space and the Bures metric to the setting of non-unital C*-algebras equipped with a faithful trace and prove that the Bures metric is also a metric in this…

We show that if X is a finite dimensional locally compact Hausdorff space, then the crossed product of C_0(X) by any automorphism has finite nuclear dimension. This generalizes previous results, in which the automorphism was required to be…

A tiling with infinite rotational symmetry, such as the Conway-Radin Pinwheel Tiling, gives rise to a topological dynamical system to which an \'etale equivalence relation is associated. A groupoid C*-algebra for a tiling is produced and a…

We construct quantum metric structures on unital AF algebras with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite dimensional C*-algebras for the quantum…

Various limit-free formulas are given for the computation of the algebraic and the topological entropy, respectively in the settings of endomorphisms of locally finite discrete groups and of continuous endomorphisms of totally disconnected…

The first author and Latr\'emoli\`ere had introduced a quantum metric (in the sense of Rieffel) on the algebra of complex-valued continuous functions on the Cantor space. We show that this quantum metric is distinct from the quantum metric…

The paper is a survey of dynamical entropy of automorphisms of operator algebras. We describe the different entropies of Connes-Stormer, Connes-Narnhofer-Thirring, Sauvageot-Thouvenot, and Voiculescu, and discuss the main examples of the…

We show that unital simple C*-algebras with tracial topological rank zero which are locally approximated by subhomogeneous C^-algebras can be classified by their ordered $K$-theory. We apply this classification result to show that certain…

We find the range of a trace on the $K_0$ group of a crossed product by a time-$t$ automorphism of a mapping torus. We also find a formula to compute the Voiculescu-Brown entropy for such an automorphism. By specializing to the commutative…

Given a unital inductive limit of C*-algebras for which each C*-algebra of the inductive sequence comes equipped with a compact quantum metric of Rieffel, we produce sufficient conditions to build a compact quantum metric on the inductive…

We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover,…

We give examples of minimal diffeomorphisms of compact connected manifolds which are not topologically orbit equivalent, but whose transformation group C*-algebras are isomorphic. The examples show that the following properties of a minimal…