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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Iterates of holomorphic self-maps of the unit ball in Hilbert space


Author: Adam Stachura
Journal: Proc. Amer. Math. Soc. 93 (1985), 88-90
MSC: Primary 47H99; Secondary 32H15, 46G20
MathSciNet review: 766533
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Abstract: An example is given of a biholomorphic self-mapping $ T$ of the unit ball in infinite-dimensional Hilbert space satisfying $ 0 = \lim {\inf _n}\left\Vert {{T^n}\left( 0 \right)} \right\Vert < \lim {\sup _n}\vert\vert{T^n}(0)\vert\vert = 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0766533-5
PII: S 0002-9939(1985)0766533-5
Keywords: Holomorphic mappings, hyperbolic metric, isometric mappings, fixed points
Article copyright: © Copyright 1985 American Mathematical Society