The Denjoy-Wolff theorem in the open unit ball of a strictly convex Banach space

摘要

Let X be a complex strictly convex Banach space with an open unit ball B. For each compact, holomorphic and fixed-point-free mapping f: B --> B there exists xi is an element of partial derivative B such that the sequence {f(n)} of iterates of f converges locally uniformly on B to the constant map taking the value xi. (C) 1999 Academic Press. [References: 34]