A Denjoy-Wolff theorem for bounded symmetric domains

TL;DR

This paper extends the classical Denjoy-Wolff theorem, originally for the unit disc, to a broader class of complex Banach spaces called bounded symmetric domains, providing new insights into fixed-point free holomorphic maps.

Contribution

It introduces a generalization of the Denjoy-Wolff theorem applicable to bounded symmetric domains of finite rank in complex Banach spaces.

Findings

Generalization of the Denjoy-Wolff theorem to bounded symmetric domains

Characterization of fixed-point free holomorphic self-maps in these domains

New fixed-point iteration results in complex Banach spaces

Abstract

We generalise the Denjoy-Wolff theorem for a fixed-point free holomorphic self-map on the complex unit disc to bounded symmetric domains of finite rank in complex Banach spaces.