This is an announcement for the paper "Kruglov operator and operators defined by random permutations" by S.V. Astashkin, D.V. Zanin, E.M. Semenov, and F.A. Sukochev.

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.

Archive classification: math.FA

Mathematics Subject Classification: 46E30

Remarks: translated from original Russian text

Submitted from: zani0005@csem.flinders.edu.au

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1003.2009

or

http://arXiv.org/abs/1003.2009