Finite representability of $\ell _p$-spaces in symmetric spaces
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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
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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