Lamel, Bernhard Local automorphisms of the Hilbert ball. (English) Zbl 1143.32010 Proc. Am. Math. Soc. 136, No. 8, 2815-2822 (2008). 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. Cited in 1 Document 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 PDFBibTeX XMLCite \textit{B. Lamel}, Proc. Am. Math. Soc. 136, No. 8, 2815--2822 (2008; Zbl 1143.32010) Full Text: DOI arXiv References: [1] H. Alexander, Holomorphic mappings from the ball and polydisc, Math. Ann. 209 (1974), 249 – 256. · Zbl 0272.32006 · doi:10.1007/BF01351851 [2] M. S. Baouendi, P. Ebenfelt, and Linda Preiss Rothschild, Parametrization of local biholomorphisms of real analytic hypersurfaces, Asian J. Math. 1 (1997), no. 1, 1 – 16. · Zbl 0943.32021 · doi:10.4310/AJM.1997.v1.n1.a1 [3] M. S. Baouendi, P. Ebenfelt, and Linda Preiss Rothschild, Local geometric properties of real submanifolds in complex space, Bull. Amer. Math. Soc. (N.S.) 37 (2000), no. 3, 309 – 336. · Zbl 0955.32027 [4] Seán Dineen, Complex analysis on infinite-dimensional spaces, Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 1999. · Zbl 1034.46504 [5] André Renaud, Quelques propriétés des applications analytiques d’une boule de dimension infinie dans une autre, Bull. Sci. Math. (2) 97 (1973), 129 – 159 (1974) (French). · Zbl 0276.32015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.