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Funktsional'nyi Analiz i ego Prilozheniya, 2009, Volume 43, Issue 2, Pages 3–18
DOI: https://doi.org/10.4213/faa2947 (Mi faa2947) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Kruglov Operator and Operators Defined by Random Permutations

S. V. Astashkina, D. V. Zaninb, E. M. Semenovc, F. A. Sukochevd

a Samara State University
b School of Informatics and Engineering at Flinders University
c Voronezh State University
d University of New South Wales, School of Mathematics and Statistics
Full-text PDF (258 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa2947
Abstract: The Kruglov property and the Kruglov operator play an important role in the study of geometric properties of r. i. function spaces. We prove that the boundedness of the Kruglov operator in an r. i. space is equivalent to the uniform boundedness on this space of a sequence of operators defined by random permutations. It is also shown that there is no minimal r. i. space with the Kruglov property.
Keywords: rearrangement invariant (r. i.) space, Orlicz, Marcinkiewicz, Lorentz spaces, Kruglov property, Kruglov operator, independent functions.
Received: 28.11.2007
English version:
Functional Analysis and Its Applications, 2009, Volume 43, Issue 2, Pages 83–95
DOI: https://doi.org/10.1007/s10688-009-0013-2
Bibliographic databases:
Document Type: Article
UDC: 517.5+517.982
Language: Russian
Citation: S. V. Astashkin, D. V. Zanin, E. M. Semenov, F. A. Sukochev, “Kruglov Operator and Operators Defined by Random Permutations”, Funktsional. Anal. i Prilozhen., 43:2 (2009), 3–18; Funct. Anal. Appl., 43:2 (2009), 83–95
Citation in format AMSBIB
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\pages 3--18
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  • https://doi.org/10.4213/faa2947
  • https://www.mathnet.ru/eng/faa/v43/i2/p3
    • This publication is cited in the following 4 articles:
    1. Sergey V. Astashkin, The Rademacher System in Function Spaces, 2020, 419  crossref
    2. Astashkin S.V., Sukochev F.A., “Randomized Operators on
      n×n
      n n Matrices and Applications”, Integr. Equ. Oper. Theory, 86:3 (2016), 333–358  crossref  mathscinet  zmath  isi  elib  scopus
    3. Astashkin S., Sukochev F., Wong Ch.P., “Disjointification of martingale differences and conditionally independent random variables with some applications”, Studia Math., 205:2 (2011), 171–200  crossref  mathscinet  zmath  isi  elib  scopus
    4. S. V. Astashkin, F. A. Sukochev, “Independent functions and the geometry of Banach spaces”, Russian Math. Surveys, 65:6 (2010), 1003–1081  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Full-text PDF :241
    References:100
    First page:13
     
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