2006/12/22 by Bernhard Lamel, Lamel, Bernhard
Mathematics · #32H12 #46G20 #46T25 #58C10 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:32H12 #msc:46G20 #msc:46T25 #msc:58C10
paper · pdf · doi:10.48550/arxiv.math/0612688
arxiv created 2006/12/22 · arxiv updated 2009/12/01
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.