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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Automorphism groups of bounded domains in Banach spaces

Authors: Stephen J. Greenfield and Nolan R. Wallach
Journal: Trans. Amer. Math. Soc. 166 (1972), 45-57
MSC: Primary 32K05; Secondary 32N15, 46B99, 58B10
MathSciNet review: 0296359
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Abstract: We prove a weak Schwarz lemma in Banach space and use it to show that in Hilbert space a Siegel domain of type II is not necessarily biholomorphic to a bounded domain. We use a strong Schwarz lemma of L. Harris to find the full group of automorphisms of the infinite dimensional versions of the Cartan domains of type I. We then show that all domains of type I are holomorphically inequivalent, and are different from k-fold products of unit balls $ (k \geqq 2)$. Other generalizations and comments are given.

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Keywords: Hilbert space, Banach space, unit balls, inequivalence of polyballs, Cartan domains, Siegel domains, Schwarz lemma
Article copyright: © Copyright 1972 American Mathematical Society