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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Iteration of compact holomorphic maps
on a Hilbert ball


Authors: Cho-Ho Chu and Pauline Mellon
Journal: Proc. Amer. Math. Soc. 125 (1997), 1771-1777
MSC (1991): Primary 46G20, 32A10, 32A17; Secondary 32M15
MathSciNet review: 1372026
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Abstract | References | Similar Articles | Additional Information

Abstract: Given a compact holomorphic fixed-point-free self-map, $f$, of the open unit ball of a Hilbert space, we show that the sequence of iterates, $(f^n)$, converges locally uniformly to a constant map $\xi $ with $\Vert \xi \Vert = 1$. This extends results of Denjoy (1926), Wolff (1926), Hervé (1963) and MacCluer (1983). The result is false without the compactness assumption, nor is it true for all open balls of $J^{*}$-algebras.


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Additional Information

Cho-Ho Chu
Affiliation: Goldsmiths College, University of London, London SE14 6NW, England
Email: maa01chc@gold.ac.uk

Pauline Mellon
Affiliation: Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland
Email: pmellon@irlearn.ucd.ie

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03761-1
PII: S 0002-9939(97)03761-1
Received by editor(s): December 27, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society