Category theorems for stable operators on Hilbert spaces
Functional Analysis
2008-07-21 v1 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.0805.1016,
title = {Category theorems for stable operators on Hilbert spaces},
author = {Tanja Eisner and Andras Sereny},
journal= {arXiv preprint arXiv:0805.1016},
year = {2008}
}
Comments
9 pages. To appear in Acta Scientiarum Mathematicarum (Szeged)