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Local automorphisms of the Hilbert ball. (English) Zbl 1143.32010

Summary: 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.

MSC:

32H12 Boundary uniqueness of mappings in several complex variables
46G20 Infinite-dimensional holomorphy
46T25 Holomorphic maps in nonlinear functional analysis
58C10 Holomorphic maps on manifolds
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References:

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