Title :

Hilbertian Jamison sequences and rigid dynamical systems

Author(s) :

Eisner, Tanja [Auteur]
Leipzig University / Universität Leipzig
Grivaux, Sophie [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Functional Analysis

Pages :

2013-2052

Publisher :

Elsevier

Publication date :

2011-10

ISSN :

0022-1236

English keyword(s) :

Linear dynamical systems
partially power-bounded operators
point spectrum of operators
hypercyclicity
weak mixing and rigid dynamical systems
topologically rigid dynamical systems

HAL domain(s) :

Mathématiques [math]/Systèmes dynamiques [math.DS]

English abstract : [en]

A strictly increasing sequence (n k) k≥0 of positive integers is said to be a Hilbertian Jamison sequence if for any bounded operator T on a separable Hilbert space such that sup k≥0 ||T n k || < +∞, the set of eigenvalues ...
Show more >A strictly increasing sequence (n k) k≥0 of positive integers is said to be a Hilbertian Jamison sequence if for any bounded operator T on a separable Hilbert space such that sup k≥0 ||T n k || < +∞, the set of eigenvalues of modulus 1 of T is at most countable. We first give a complete characterization of such sequences. We then turn to the study of rigidity sequences (n k) k≥0 for weakly mixing dynamical systems on measure spaces, and give various conditions, some of which are closely related to the Jamison condition, for a sequence to be a rigidity sequence. We obtain on our way a complete characterization of topological rigidity and uniform rigidity sequences for linear dynamical systems, and we construct in this framework examples of dynamical systems which are both weakly mixing in the measure-theoretic sense and uniformly rigid.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T15:33:48Z