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

 

Local automorphisms of the Hilbert ball


Author: Bernhard Lamel
Journal: Proc. Amer. Math. Soc. 136 (2008), 2815-2822
MSC (2000): Primary 32H12, 46G20, 46T25, 58C10
Published electronically: April 14, 2008
MathSciNet review: 2399045
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Abstract: Every holomorphic mapping which takes a piece of the boundary of the unit ball in complex Hilbert space into the boundary of the unit ball and whose differential at some point of this boundary is onto is the restriction of an automorphism of the ball. We also show that it is enough to assume that the mapping is only Gâteaux-holomorphic.


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Additional Information

Bernhard Lamel
Affiliation: Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Österreich
Email: bernhard.lamel@univie.ac.at

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09440-9
PII: S 0002-9939(08)09440-9
Received by editor(s): November 21, 2006
Published electronically: April 14, 2008
Additional Notes: The author was supported by the Austrian Science Fund FWF, Projects P17111 and P19667
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.