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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Automorphism groups of bounded domains in Banach spaces
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by Stephen J. Greenfield and Nolan R. Wallach PDF
Trans. Amer. Math. Soc. 166 (1972), 45-57 Request permission

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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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 166 (1972), 45-57
  • MSC: Primary 32K05; Secondary 32N15, 46B99, 58B10
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0296359-6
  • MathSciNet review: 0296359