We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geometri...

We give algebraic characterizations for expansiveness of algebraic actions of countable groups. The notion of p-expansiveness is introduced for algebraic actions, and we show that for countable amenable groups, a finitely presented algebraic action is 1-expansive exactly when it has finite entropy. We also study the local entropy theory for actions of countable amenable groups on compact groups...

We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces as discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geome...

M. Murakami, M.R. Wade, J.C. DeBoo, C.M. Greenfield, T.C. Luce, M.A. Makowski, C.C. Petty, G.M. Staebler, T.S. Taylor, M.E. Austin, D.R. Baker, R.V. Budny, K.H. Burrell, T.A. Casper, M. Choi, J.R. Ferron, A.M. Garofalo, I.A. Gorelov, R.J. Groebner, R. La Haye, A.W. Hyatt, R.J. Jayakumar, K. Kajiwara, J.E. Kinsey, L.L. Lao, J. Lohr, D. McCune, R.I. Pinsker, P.A. Politzer, R. Prater, ( b ) H.E. S...

1. Gel’fand, S., Pinsker, M.: Coding for channel with random parameters. Problems of Control and Information Theory 9 (1980) 19–31 2. Eggers, J., Su, J., Girod, B.: A blind watermarking scheme based on structured codebooks. In: Secure Images and Image Authentication, IEE Colloquium, London, UK (2000) 4/1–4/6 Conclusions and Future Work • Halftone quantization: it exploits the fact that there ex...

Bernhard Banaschewski McMaster University William DeMeo University of South Carolina François Dorais Dartmouth College Mart́ın Escardó University of Birmingham Mai Gehrke Université Diderot Paris 7 & CNRS Steven Givant Mills College Heinz-Peter Gumm Universität Marburg Steve Jackson University of North Texas Michael Pinsker Université Diderot Paris 7 Hilary Priestley University of Oxford Dima Si...

We demonstrate a probabilistic construction of binary linear codes meeting the GilbertVarshamov bound (with overwhelming probability) for rates up to about 10−4, together with polynomial time algorithms to perform encoding and decoding up to half the distance. This is the first such result (for some positive rate) with polynomial decoding complexity; previously a similar result (up to rate abou...

We characterize positive topological entropy for quasi-state space homeomorphisms induced from C∗-algebra automorphisms in terms of dynamically generated subspaces isomorphic to l1. This geometric condition is also used to give a description of the topological Pinsker algebra. In particular we obtain a geometric characterization of positive entropy for topological dynamical systems, as well as ...