English

The generalized Berger-Wang formula and the spectral radius of linear cocycles

Dynamical Systems 2009-06-17 v1 Functional Analysis

Abstract

Using multiplicative ergodic theory we prove two formulae describing the relationships between different joint spectral radii for sets of bounded linear operators acting on a Banach space. In particular we recover a formula previously proved by V. S. Shulman and Yu. V. Turovski\u{\i} using operator-theoretic ideas. As a byproduct of our method we answer a question of J. E. Cohen on the limiting behaviour of the spectral radius of a measurable matrix cocycle.

Keywords

Cite

@article{arxiv.0906.2915,
  title  = {The generalized Berger-Wang formula and the spectral radius of linear cocycles},
  author = {Ian D. Morris},
  journal= {arXiv preprint arXiv:0906.2915},
  year   = {2009}
}