Annales Academię Scientiarum Fennicę
Mathematica
Volumen 38, 2013, 747-756

A DENJOY-WOLFF THEOREM FOR COMPACT HOLOMORPHIC MAPPINGS IN COMPLEX BANACH SPACES

Monika Budzynska, Tadeusz Kuczumow and Simeon Reich

Uniwersytet Marii Curie-Sklodowskiej, Instytut Matematyki
20-031 Lublin, Poland; monikab1 'at' hektor.umcs.lublin.pl

Uniwersytet Marii Curie-Sklodowskiej, Instytut Matematyki
20-031 Lublin, Poland; tadek 'at' hektor.umcs.lublin.pl

The Technion - Israel Institute of Technology, Department of Mathematics
32000 Haifa, Israel; sreich 'at' tx.technion.ac.il

Abstract. We establish a Denjoy-Wolff theorem for compact holomorphic self-mappings of bounded and strictly convex domains in arbitrary complex Banach spaces.

2010 Mathematics Subject Classification: Primary 32A10, 46G20, 46T25, 47H09, 47H10.

Key words: Banach space, compact mapping, Denjoy-Wolff theorem, fixed point, holomorphic mapping, horosphere, iterates of holomorphic mappings, k_D-nonexpansive mapping, Kobayashi distance, strictly convex domain.

Reference to this article: M. Budzynska, T. Kuczumow and S. Reich: A Denjoy-Wolff theorem for compact holomorphic mappings in complex Banach spaces. Ann. Acad. Sci. Fenn. Math. 38 (2013), 747-756.

Full document as PDF file

doi:10.5186/aasfm.2013.3846

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