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arXiv · 0909.4695

Rigidity of contractions on Hilbert spaces

Tanja Eisner
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Abstract

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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Tanja Eisner. 2009-09-25. Rigidity of contractions on Hilbert spaces. https://arxiv.org/abs/0909.4695

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