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Mat. Sb., 2004, Volume 195, Number 2, Pages 117–140 (Mi msb802)  

This article is cited in 21 scientific papers (total in 21 papers)

The Banach–Saks index

E. M. Semenova, F. A. Sukochevb

a Voronezh State University
b Flinders University

Abstract: The properties of the Banach–Saks index are studied in the class of rearrangement invariant spaces. The Banach–Saks indices of the spaces $L_{p,q}$ and some Orlicz spaces are calculated. Generalizations of the Banach–Saks theorems are obtained.

DOI: https://doi.org/10.4213/sm802

Full text: PDF file (368 kB)
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English version:
Sbornik: Mathematics, 2004, 195:2, 263–285

Bibliographic databases:

UDC: 517.982
MSC: 46E30
Received: 23.06.2003

Citation: E. M. Semenov, F. A. Sukochev, “The Banach–Saks index”, Mat. Sb., 195:2 (2004), 117–140; Sb. Math., 195:2 (2004), 263–285

Citation in format AMSBIB
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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., Semenov E.M., Sukochev F.A., “The Banach-Saks $p$-property”, Math. Ann., 332:4 (2005), 879–900  crossref  mathscinet  zmath  isi  elib
    2. E. M. Semenov, F. A. Sukochev, “Svoistvo Banakha — Saksa”, Vladikavk. matem. zhurn., 7:3 (2005), 64–70  mathnet  mathscinet
    3. E. M. Semenov, F. A. Sukochev, “Estimation of a quadratic function and the $p$-Banach–Saks property”, St. Petersburg Math. J., 18:4 (2007), 647–656  mathnet  crossref  mathscinet  zmath  elib
    4. Hernández F.L., Sánchez V.M., Semenov E.M., “Strictly singular inclusions into $L^1+L^\infty$”, Math. Z., 258:1 (2007), 87–106  crossref  mathscinet  isi
    5. Lust-Piquard F., Sukochev F., “The $p$-Banach Saks property in symmetric operator spaces”, Illinois J. Math., 51:4 (2007), 1207–1229  mathscinet  zmath  isi
    6. Astashkin S.V., Sukochev F.A., “Banach-Saks property in Marcinkiewicz spaces”, J. Math. Anal. Appl., 336:2 (2007), 1231–1258  crossref  mathscinet  zmath  isi  elib
    7. 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
    8. A. I. Novikova, E. M. Semenov, F. A. Sukochev, “Banach-Saks index in spaces with symmetric basis”, Dokl. Math., 77:3 (2008), 396–397  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    9. 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
    10. Astashkin S.V., Semenov E.M., Sukochev F.A., “Banach-Saks type properties in rearrangement-invariant spaces with the Kruglov property”, Houston J. Math., 35:3 (2009), 959–973  mathscinet  zmath  isi  elib
    11. A. I. Novikova, “Indeksy Banakha–Saksa dlya podprostranstv Rademakhera”, Vestn. SamGU. Estestvennonauchn. ser., 2009, no. 4(70), 44–51  mathnet
    12. Hernández F.L., Semenov E.M., Tradacete P., “Strictly singular operators on $L^p$ spaces and interpolation”, Proc. Amer. Math. Soc., 138:2 (2010), 675–686  crossref  mathscinet  zmath  isi
    13. A. I. Novikova, “The Banach–Saks index of some sequence spaces”, Siberian Math. J., 51:2 (2010), 296–300  mathnet  crossref  mathscinet  isi  elib  elib
    14. Astashkin S.V., Sukochev F.A., Wong C.P., “Distributionally Concave Symmetric Spaces and Uniqueness of Symmetric Structure”, Adv. Math., 232:1 (2013), 399–431  crossref  mathscinet  zmath  isi  elib
    15. A. Kamińska, Han Ju Lee, “The Banach-Saks properties in Orlicz-Lorentz spaces”, Abstr. Appl. Anal., 2014 (2014), 423198, 8 pp.  crossref  mathscinet  isi
    16. A. Kamińska, Han Ju Lee, “Banach-Saks properties of Musielak-Orlicz and Nakano sequence spaces”, Proc. Amer. Math. Soc., 142:2 (2014), 547–558  mathscinet  zmath  isi
    17. A. Kuryakov, F. Sukochev, “Isomorphic classification of <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow></mml:msub></mml:math>-spaces”, Journal of Functional Analysis, 2015  crossref  mathscinet
    18. Jiao Y., Sukochev F., Zanin D., Zhou D., “Johnson–Schechtman inequalities for noncommutative martingales”, J. Funct. Anal., 272:3 (2017), 976–1016  crossref  mathscinet  zmath  isi  scopus
    19. Chilin V., Litvinov S., “Individual ergodic theorems in noncommutative Orlicz spaces”, Positivity, 21:1 (2017), 49–59  crossref  mathscinet  zmath  isi  scopus
    20. Hernandez F.L., Semenov E.M., Tradacete P., “Interpolation and Extrapolation of Strictly Singular Operators Between l-P Spaces”, Adv. Math., 316 (2017), 667–690  crossref  mathscinet  zmath  isi  scopus
    21. Sadovskaya O., Sukochev F., “Isomorphic Classification of l-P,l-Q-Spaces: the Case P=2, 1 <= Q < 2”, Proc. Amer. Math. Soc., 146:9 (2018), 3975–3984  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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