4,860 research outputs found
Dimension and dynamical entropy for metrized C*-algebras
We introduce notions of dimension and dynamical entropy for unital
C*-algebras ``metrized'' by means of c-Lip-norms, which are complex-scalar
versions of the Lip-norms constitutive of Rieffel's compact quantum metric
spaces. Our examples involve UHF algebras and noncommutative tori. In
particular we show that the entropy of a noncommutative toral automorphism with
respect to the canonical c-Lip-norm coincides with the topological entropy of
its commutative analogue.Comment: To appear in Commun. Math. Phys., 33 page
Matricial quantum Gromov-Hausdorff distance
We develop a matricial version of Rieffel's Gromov-Hausdorff distance for
compact quantum metric spaces within the setting of operator systems and unital
C*-algebras. Our approach yields a metric space of ``isometric'' unital
complete order isomorphism classes of metrized operator systems which in many
cases exhibits the same convergence properties as those in the quantum metric
setting, as for example in Rieffel's approximation of the sphere by matrix
algebras using Berezin quantization. Within the metric subspace of metrized
unital C*-algebras we establish the convergence of sequences which are Cauchy
with respect to a larger Leibniz distance, and we also prove an analogue of the
precompactness theorems of Gromov and Rieffel.Comment: 29 page
Independence in topological and C*-dynamics
We develop a systematic approach to the study of independence in topological
dynamics with an emphasis on combinatorial methods. One of our principal aims
is to combinatorialize the local analysis of topological entropy and related
mixing properties. We also reframe our theory of dynamical independence in
terms of tensor products and thereby expand its scope to C*-dynamics.Comment: 54 pages; Definition 2.2 changed; to appear in Mathematische Annale
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