Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Asymptotic properties of Banach spaces under renormings
HTML articles powered by AMS MathViewer

by E. Odell and Th. Schlumprecht
J. Amer. Math. Soc. 11 (1998), 175-188


It is shown that a separable Banach space $X$ can be given an equivalent norm $||| \cdot |||$ with the following properties: If $(x_{n})\subseteq X$ is relatively weakly compact and $\lim _{m\to \infty } \lim _{n\to \infty } ||| x_{m}+x_{n}||| = 2\lim _{m\to \infty } ||| x_{m}|||$, then $(x_{n})$ converges in norm. This yields a characterization of reflexivity once proposed by V.D. Milman. In addition it is shown that some spreading model of a sequence in $(X,||| \cdot ||| )$ is 1-equivalent to the unit vector basis of $\ell _{1}$ (respectively, $c_{0}$) implies that $X$ contains an isomorph of $\ell _{1}$ (respectively, $c_{0}$).
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 46B03, 46B45
  • Retrieve articles in all journals with MSC (1991): 46B03, 46B45
Bibliographic Information
  • E. Odell
  • Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712-1082
  • Email:
  • Th. Schlumprecht
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
  • MR Author ID: 260001
  • Email:
  • Received by editor(s): May 12, 1997
  • Received by editor(s) in revised form: September 15, 1997
  • Additional Notes: Research of both authors was supported by NSF and TARP
  • © Copyright 1998 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 11 (1998), 175-188
  • MSC (1991): Primary 46B03, 46B45
  • DOI:
  • MathSciNet review: 1469118