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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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Szlenk indices and uniform homeomorphisms
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by G. Godefroy, N. J. Kalton and G. Lancien PDF
Trans. Amer. Math. Soc. 353 (2001), 3895-3918 Request permission


We prove some rather precise renorming theorems for Banach spaces with Szlenk index $\omega _0.$ We use these theorems to show the invariance of certain quantitative Szlenk-type indices under uniform homeomorphisms.
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Additional Information
  • G. Godefroy
  • Affiliation: Equipe d’Analyse, Université Paris VI, Boite 186, 4, Place Jussieu, 75252 Paris Cedex 05, France
  • Email:
  • N. J. Kalton
  • Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
  • Email:
  • G. Lancien
  • Affiliation: Equipe de Mathématiques - UMR 6623, Université de Franche-Comté, F-25030 Besançon cedex
  • MR Author ID: 324078
  • Email:
  • Received by editor(s): June 15, 1999
  • Received by editor(s) in revised form: July 3, 2000
  • Published electronically: May 17, 2001
  • Additional Notes: The second author was supported by NSF grant DMS-9870027.
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 3895-3918
  • MSC (2000): Primary 46B03, 46B20
  • DOI:
  • MathSciNet review: 1837213