[Banach] Abstract of a paper by David Kerr and Hanfeng Li

[Dale Alspach]

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 at math.uni-muenster.de

The paper may be downloaded from the archive by web browser from URL

 http://front.math.ucdavis.edu/math.FA/0407386

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

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 to: math at arXiv.org.