Local automorphisms of the Hilbert ball

Lamel, Bernhard

doi:10.1090/S0002-9939-08-09440-9

Local automorphisms of the Hilbert ball
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by Bernhard Lamel

Proc. Amer. Math. Soc. 136 (2008), 2815-2822

DOI: https://doi.org/10.1090/S0002-9939-08-09440-9

Published electronically: 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.

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