This is an announcement for the paper "Dynamical entropy in Banach spaces" by David Kerr and Hanfeng Li.

Abstract: 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 geometrically and topologically. This leads to various applications; for example, we obtain a geometric description of the topological Pinsker factor and show that a C*-algebra is type I if and only if every multiplier inner *-automorphism has zero CA entropy. We also examine the behaviour of CA entropy under various product constructions and determine its value in many examples, including isometric automorphisms of l_p spaces and noncommutative tensor product shifts.

Archive classification: Functional Analysis; Dynamical Systems; Operator Algebras

Remarks: 40 pages; subsumes the material from math.DS/0303161

The source file(s), CA13.tex: 144163 bytes, is(are) stored in gzipped form as 0407386.gz with size 41kb. The corresponding postcript file has gzipped size 162kb.

Submitted from: kerr@math.uni-muenster.de

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http://arXiv.org/abs/math.FA/0407386

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