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Local automorphisms of the Hilbert ball
Author(s):
Bernhard
Lamel
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2815-2822.
MSC (2000):
Primary 32H12, 46G20, 46T25, 58C10
Posted:
April 14, 2008
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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.
References:
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- 2.
- M. S. Baouendi, P. Ebenfelt, and L. P. Rothschild, Parametrization of local biholomorphisms of real analytic hypersurfaces, Asian J. Math. 1 (1997), no. 1, 1-16. MR 99b:32022
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- -, Local geometric properties of real submanifolds in complex space, Bull. Amer. Math. Soc. (N.S.) 37 (2000), no. 3, 309-336 (electronic). MR 2001a:32043
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- S. Dineen, Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer-Verlag London Ltd., London, 1999. MR 1705327 (2001a:46043)
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- A. Renaud, Quelques propriétés des applications analytiques d'une boule de dimension infinie dans une autre, Bull. Sci. Math. (2) 97 (1973), 129-159 (1974). MR 0338455 (49:3219)
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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:
10.1090/S0002-9939-08-09440-9
PII:
S 0002-9939(08)09440-9
Received by editor(s):
November 21, 2006
Posted:
April 14, 2008
Additional Notes:
The author was supported by the Austrian Science Fund FWF, Projects P17111 and P19667
Communicated by:
Mei-Chi Shaw
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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