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

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\uı 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.

References in corpus (1)

• A formula with some applications to the theory of Lyapunov exponents

Cited by in corpus (8)

• The Berger-Wang formula for the Markovian joint spectral radius
• Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles
• A Gel'fand-type spectral radius formula and stability of linear constrained switching systems
• A semi-invertible Oseledets Theorem with applications to transfer operator cocycles
• Robust periodic stability implies uniform exponential stability of Markovian jump linear systems and random linear ordinary differential equations
• Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms
• Topological radicals, III. Joint spectral radius
• Inequalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators