Hilbertian Jamison sequences and rigid dynamical systems

By Tatjana Eisner, S. Grivaux. 2011

46 citations recorded by the source corpus.

A strictly increasing sequence (n_k) of positive integers is said to be a Hilbertian Jamison sequence if for any bounded operator T on a separable Hilbert space such that the supremum over k of the norms ||T^{n_k}|| is finite, 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) 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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bc1a7ea4515d93aab220159eeca280c6aeb0d3c6

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Mixing operators and small subsets of the circle (2011, background): “This line of investigations was pursued even much further in [4] and [24].”
Recurrent Linear Operators (2013, background): “These notions have also been studied in linear dynamics for example in [19,20].”