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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Finite representability of $\ell _p$-spaces in symmetric spaces
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by S. V. Astashkin
Translated by: S. Kislyakov
St. Petersburg Math. J. 23 (2012), 257-273
DOI: https://doi.org/10.1090/S1061-0022-2012-01196-9
Published electronically: January 23, 2012

Abstract:

For a separable rearrangement invariant space $X$ on the semiaxis, ${\mathcal F}(X)$ is defined to be the set of all $p\in [1,\infty ]$ such that $\ell _p$ is finitely representable in $X$ in such a way that the standard basis vectors of $\ell _p$ correspond to equimeasurable mutually disjoint functions. In the paper, a characterization of the set ${\mathcal F}(X)$ is obtained. As a consequence, a version of Krivine’s well-known theorem is proved for rearrangement invariant spaces. Next, a description of the sets ${\mathcal F}(X)$ for certain Lorentz spaces is found.
References
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Bibliographic Information
  • S. V. Astashkin
  • Affiliation: Samara State University, ul. Akademika Pavlova 1, Samara 443011, Russia
  • MR Author ID: 197703
  • Email: astashkn@ssu.samara.ru
  • Received by editor(s): October 7, 2009
  • Published electronically: January 23, 2012
  • Additional Notes: Supported in part by RFBR, grant no. 07-01-96603
  • © Copyright 2012 American Mathematical Society
  • Journal: St. Petersburg Math. J. 23 (2012), 257-273
  • MSC (2010): Primary 46E30
  • DOI: https://doi.org/10.1090/S1061-0022-2012-01196-9
  • MathSciNet review: 2841673