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Category theorems for stable semigroups

Published online by Cambridge University Press:  01 April 2009

TANJA EISNER  and
ANDRÁS SERÉNY
TANJA EISNER
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076, Tübingen, Germany (email: talo@fa.uni-tuebingen.de)
ANDRÁS SERÉNY
Affiliation:
Department of Mathematics and its Applications, Central European University, Nádor utca 9, H-1051 Budapest, Hungary (email: sandris@elte.hu)
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Abstract

Inspired by the classical category theorems of Halmos and Rohlin for discrete measure-preserving transformations, we prove analogous results in the abstract setting of unitary and isometric C0-semigroups on a separable Hilbert space. More precisely, we show that, for an appropriate topology, the set of all weakly stable unitary groups (isometric semigroups) is of first category, while the set of all almost weakly stable unitary groups (isometric semigroups) is residual.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 2 , April 2009 , pp. 487 - 494
Copyright
Copyright © Cambridge University Press 2008

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