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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
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
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
Linking options:
https://www.mathnet.ru/eng/faa2947https://doi.org/10.4213/faa2947 https://www.mathnet.ru/eng/faa/v43/i2/p3
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