Category theorems for stable operators on Hilbert spaces

Acta Sci. Math. (Szeged) 74 (2008), 259-270. We discuss the two closely related, but different concepts of weak and almost weak stability for the powers of a contraction on a separable Hilbert space. Extending Halmos' and Rohlin's theorems in ergodic theory as a model, we show that the set...

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Bibliographic Details
Main Authors Eisner, Tanja, Sereny, Andras
Format Journal Article
LanguageEnglish
Published 07.05.2008
Subjects
Mathematics - Dynamical Systems
Mathematics - Functional Analysis
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Summary:Acta Sci. Math. (Szeged) 74 (2008), 259-270. We discuss the two closely related, but different concepts of weak and almost weak stability for the powers of a contraction on a separable Hilbert space. Extending Halmos' and Rohlin's theorems in ergodic theory as a model, we show that the set of all weakly stable contractions is of first category while the set of all almost weakly stable contractions is of second category and is residual. Analogous statements for unitary and isometric operators are also proved.
DOI:10.48550/arxiv.0805.1016