Rigidity of contractions on Hilbert spaces

Original · EN

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 Tⁿʲ converges weakly to zero along a sequence {nⱼ} with density one. The continuous analogue is presented for isometric ang unitary C₀-(semi)groups.