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Algebra i Analiz, 2006, Volume 18, Issue 4, Pages 185–197 (Mi aa82)  

This article is cited in 3 scientific papers (total in 3 papers)

Research Papers

Estimation of a quadratic function and the $p$-Banach–Saks property

E. M. Semenova, F. A. Sukochevb

a Voronezh State University
b Flinders University of SA, Bedford Park, SA, Australia

Abstract: Let $E$ be a rearrangement-invariant Banach function space on $[0,1]$, and let $\Gamma(E)$ denote the set of all $p\ge 1$ such that any sequence $\{x_n\}$ in $E$ converging weakly to 0 has a subsequence $\{y_n\}$ with $\sup_m m^{-1/p}\|\sum_{1\le k\le m}y_n\|<\infty$. The set $\Gamma_i(E)$ is defined similarly, but only sequences $\{x_n\}$ of independent random variables are taken into account. It is proved (under the assumption $\Gamma(E)\ne\{1\}$) that if $\Gamma_i(E)\setminus\Gamma(E)\ne\varnothing$, then $\Gamma_i(E)\setminus\Gamma(E)=\{2\}$.

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English version:
St. Petersburg Mathematical Journal, 2007, 18:4, 647–656

Bibliographic databases:

MSC: 46E30
Received: 22.02.2006

Citation: E. M. Semenov, F. A. Sukochev, “Estimation of a quadratic function and the $p$-Banach–Saks property”, Algebra i Analiz, 18:4 (2006), 185–197; St. Petersburg Math. J., 18:4 (2007), 647–656

Citation in format AMSBIB
\Bibitem{SemSuk06}
\by E.~M.~Semenov, F.~A.~Sukochev
\paper Estimation of a quadratic function and the $p$-Banach--Saks property
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 4
\pages 185--197
\mathnet{http://mi.mathnet.ru/aa82}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2262587}
\zmath{https://zbmath.org/?q=an:1139.46011}
\elib{https://elibrary.ru/item.asp?id=9243976}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 4
\pages 647--656
\crossref{https://doi.org/10.1090/S1061-0022-07-00964-8}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Astashkin S.V., Kalton N., Sukochev F.A., “Cesaro mean convergence of martingale differences in rearrangement invariant spaces”, Positivity, 12:3 (2008), 387–406  crossref  mathscinet  zmath  isi  elib  scopus
    2. Sukochev F.A., Zanin D., “Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces”, Studia Math., 191:2 (2009), 101–122  crossref  mathscinet  zmath  isi  elib  scopus
    3. Astashkin S.V., Semenov E.M., Sukochev F., “Banach-Saks type properties in rearrangement-invariant spaces with the Kruglov property”, Houston J. Math., 35:3 (2009), 959–973  mathscinet  zmath  isi  elib
  • Алгебра и анализ St. Petersburg Mathematical Journal
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