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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 pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Weakly null sequences in $L_1$
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by William B. Johnson, Bernard Maurey and Gideon Schechtman PDF
J. Amer. Math. Soc. 20 (2007), 25-36

Abstract:

We construct a weakly null normalized sequence $\{f_i\}_{i=1}^{\infty }$ in $L_1$ so that for each $\varepsilon >0$, the Haar basis is $(1+\varepsilon )$-equivalent to a block basis of every subsequence of $\{f_i\}_{i=1}^{\infty }$. In particular, the sequence $\{f_i\}_{i=1}^{\infty }$ has no unconditionally basic subsequence. This answers a question raised by Bernard Maurey and H. P. Rosenthal in 1977. A similar example is given in an appropriate class of rearrangement invariant function spaces.
References
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Additional Information
  • William B. Johnson
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
  • MR Author ID: 95220
  • Email: johnson@math.tamu.edu
  • Bernard Maurey
  • Affiliation: Laboratoire d’Analyse et de Mathématiques Appliquées, UMR CNRS 8050, Université de Marne la Vallée, 77454 Champs-sur-Marne, France
  • Email: maurey@univ-mlv.fr
  • Gideon Schechtman
  • Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
  • MR Author ID: 155695
  • Email: gideon.schechtman@weizmann.ac.il
  • Received by editor(s): June 8, 2004
  • Published electronically: September 19, 2006
  • Additional Notes: The first author was supported in part by NSF grant DMS-0200690 and NSF grant DMS-0503688, Texas Advanced Research Program 010366-0033-20013 and the U.S.-Israel Binational Science Foundation.
    The last author was supported in part by the Israel Science Foundation and the U.S.-Israel Binational Science Foundation and was a participant in the NSF Workshop in Linear Analysis and Probability, Texas A&M University.
  • © Copyright 2006 by the authors
  • Journal: J. Amer. Math. Soc. 20 (2007), 25-36
  • MSC (2000): Primary 46B15, 46E30
  • DOI: https://doi.org/10.1090/S0894-0347-06-00548-0
  • MathSciNet review: 2257395