A version of the theorem of Johnson, Palmer, and Sell for quasicompact cocycles

Abstract

The well-known theorem of Johnson, Palmer and Sell asserts that the endpoints of the Sacker-Sell spectrum of a given cocycle of invertible matrices over a topological dynamical system (M, f ) are realized as Lyapunov exponents with respect to some ergodic invariant probability measure for f . In this note we establish the version of this result for quasicompact cocycles of operators acting on an arbitrary Banach space.2010 Mathematics Subject Classification. Primary: 37C40, 37C60.