Rigidity of contractions on Hilbert spaces

Details Rigidity of contractions on Hilbert spaces Rigidity of contractions on Hilbert spaces

2009-09-25

arxiv.org/abs/0909.4695v1

Mathematics

Functional Analysis

17 pages, submitted

Scientific paper

We study the asymptotic behaviour of contractive operators and strongly continuous semigroups on separable Hilbert spaces using the notion of rigidity. In particular, we show that a "typical" contraction $T$ contains the unit circle times the identity operator in the strong limit set of its powers, while $T^{n_j}$ converges weakly to zero along a sequence $\{n_j\}$ with density one. The continuous analogue is presented for isometric ang unitary $C_0$-(semi)groups.

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