Topologies on the set of iterates of a holomorphic function in infinite dimensions

Abstract

Let $f:B\to B$ be a compact holomorphic map on the open unit ball $B$ of a complex Banach space $Z$ in possibly infinite dimensions, where $f$ compact means $f(B)$ is relatively compact. The sequence of iterates $(f^n)_n$ of $f$ (where $f^n:=f \circ