Category theorems for stable operators on Hilbert spaces

Details Category theorems for stable operators on Hilbert spaces Category theorems for stable operators on Hilbert spaces

2008-05-07

arxiv.org/abs/0805.1016v1

Acta Sci. Math. (Szeged) 74 (2008), 259-270.

Mathematics

Functional Analysis

9 pages. To appear in Acta Scientiarum Mathematicarum (Szeged)

Scientific paper

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.

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