Kruglov operator and operators defined by random permutations
Functional Analysis
2010-03-11 v1
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 a r.i. space is equivalent to the uniform boundedness on this space of a sequence of operators defined by random permutations. It is shown also that there is no minimal r.i. space with the Kruglov property.
Keywords
Cite
@article{arxiv.1003.2009,
title = {Kruglov operator and operators defined by random permutations},
author = {S. V. Astashkin and D. V. Zanin and E. M. Semenov and F. A. Sukochev},
journal= {arXiv preprint arXiv:1003.2009},
year = {2010}
}
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