This is an announcement for the paper "Random sets of isomorphism of linear operators on Hilbert space" by Roman Vershynin.

Abstract: This note deals with a problem of the probabilistic Ramsey theory. Given a linear operator T on a Hilbert space with an orthogonal basis, we define the isomorphic structure Sigma(T) as the family of all finite subsets of the basis such that T restricted to their span is a nice isomorphism. We give an optimal bound on the size of Sigma(T). This improves and extends in several ways the principle of restricted invertibility due to Bourgain and Tzafriri. With an appropriate notion of randomness, we obtain a randomized principle of restricted invertibility.

Archive classification: Functional Analysis; Probability

Mathematics Subject Classification: 46B09

Remarks: 10 pages

The source file(s), imsart.sty: 47558 bytes, sets-of-isomorphism.tex: 27134 bytes, is(are) stored in gzipped form as 0601112.tar.gz with size 21kb. The corresponding postcript file has gzipped size 51kb.

Submitted from: vershynin@math.ucdavis.edu

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http://front.math.ucdavis.edu/math.FA/0601112

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http://arXiv.org/abs/math.FA/0601112

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