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

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

2009-06-16

arxiv.org/abs/0906.2915v1

Mathematics

Dynamical Systems

Scientific paper

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.

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