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

2009/06/16 by Ian D. Morris, Morris, Ian D. · 1 citation
Computer Science · Mathematics · #37H15 #47D03 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0906.2915

openalex publication_date 2009/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A formula with some applications to the theory of Lyapunov exponents
• Livšic Theorem for matrix cocycles

Cited by

• Asymptotic behavior of the spectral radius of locally constant strongly irreducible cocycles

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