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Funktsional. Anal. i Prilozhen., 2009, Volume 43, Issue 2, Pages 3–18 (Mi faa2947)  

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

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

DOI: https://doi.org/10.4213/faa2947

Full text: PDF file (258 kB)
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English version:
Functional Analysis and Its Applications, 2009, 43:2, 83–95

Bibliographic databases:

UDC: 517.5+517.982
Received: 28.11.2007

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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\paper Kruglov Operator and Operators Defined by Random Permutations
\jour Funktsional. Anal. i Prilozhen.
\yr 2009
\vol 43
\issue 2
\pages 3--18
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\jour Funct. Anal. Appl.
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\pages 83--95
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
    3. Astashkin S.V., Sukochev F.A., “Randomized Operators on
      $${n\times n}$$
      n n Matrices and Applications”, Integr. Equ. Oper. Theory, 86:3 (2016), 333–358  crossref  mathscinet  zmath  isi  elib  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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