Sub-additivity of measure-theoretic entropies of commuting transformations on Banach space

Abstract

We consider two commuting smooth transformations on Banach spaces, prove the sub-additivity of measure-theoretic entropies and give the condition for equality. This is an extension of Hu's work on commuting diffeomorphisms in a finite-dimensional space (HuHu Yi 1993 Ergod. Th. Dynam. Sys. 13 73-100) to the case of systems on a Banach space.