Geodesic
Kruglov Operator and Operators Defined by Random Permutations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 2, pp. 3-18

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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, Lorentz spaces, Kruglov property, Kruglov operator, independent functions.
Mots-clés : Marcinkiewicz 
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     author = {S. V. Astashkin and D. V. Zanin and E. M. Semenov and F. A. Sukochev},
     title = {Kruglov {Operator} and {Operators} {Defined} by {Random} {Permutations}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     number = {2},
     year = {2009},
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S. V. Astashkin; D. V. Zanin; E. M. Semenov; F. A. Sukochev. Kruglov Operator and Operators Defined by Random Permutations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 2, pp. 3-18. http://geodesic.mathdoc.fr/item/FAA_2009_43_2_a0/