A note on mean ergodic composition operators on spaces of holomorphic functions

Bonet Solves José Antonio, DOMANSKI P.

2011

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas

We characterize those composition operators defined on spaces of holomorphic functions of several variables which are power bounded, i.e. the orbits of all the elements are bounded. This condition is equivalent to the composition operator being mean ergodic. We also describe the form of the symbol when the composition operator is mean ergodic. © 2011 The Author(s).