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Commutant lifting and factorization of reproducing kernels
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2005 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 224, no 1, 134-159 p.Article in journal (Refereed) Published
Abstract [en]

A general version of the commutant lifting theorem for operators between different spaces is proved. It includes as special cases the lifting theorems of Ball-Trent-Vinnikov and Volberg-Treil. A multivariable variant of the Volberg-Treil theorem is obtained as a corollary. A certain factorization property of reproducing kernels is shown to be a sufficient condition for the lifting. Another factorization property is shown to be a necessary condition.

Place, publisher, year, edition, pages
2005. Vol. 224, no 1, 134-159 p.
Keyword [en]
zcommutant lifting, reproducing kernels, nevanlinna-pick kernels, hilbert-spaces, theorem, subspaces
URN: urn:nbn:se:kth:diva-14824DOI: 10.1016/j.jfa.2004.08.011ISI: 000229710300006ScopusID: 2-s2.0-18844431380OAI: diva2:332865
QC 20100525Available from: 2010-08-05 Created: 2010-08-05Bibliographically approved

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Shimorin, Serguei
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