Rigidity of contractions on Hilbert spaces

2009/09/25 by Eisner, Tanja
#28D05 #47A35 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0909.4695

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 C₀-(semi)groups.

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