Escaping a neighborhood along a prescribed sequence in Lie groups and Banach algebras

Catalin Badea, Vincent Devinck, Sophie Grivaux

Published 2019-05-23Version 1

It is shown that Jamison sequences, introduced in [C. Badea and S. Grivaux, Unimodular eigenvalues, uniformly distributed sequences and linear dynamics, Adv. Math. 211 (2007), no. 2, 766--793], arise naturally in the study of topological groups with no small subgroups, of Banach algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of its powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or Banach algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given and other related results are proved.