Local automorphisms of the Hilbert ball

Details Local automorphisms of the Hilbert ball Local automorphisms of the Hilbert ball

2006-12-22

arxiv.org/abs/math/0612688v1

Mathematics

Complex Variables

Scientific paper

We prove an analogue of Alexander's Theorem for holomorphic mappings of the unit ball in a complex Hilbert space: Every holomorphic mapping which takes a piece of the boundary of the unit ball 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 Gateaux-holomorphic.

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