Commutant lifting and factorization of reproducing kernels
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
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.
zcommutant lifting, reproducing kernels, nevanlinna-pick kernels, hilbert-spaces, theorem, subspaces
IdentifiersURN: urn:nbn:se:kth:diva-14824DOI: 10.1016/j.jfa.2004.08.011ISI: 000229710300006ScopusID: 2-s2.0-18844431380OAI: oai:DiVA.org:kth-14824DiVA: diva2:332865
QC 201005252010-08-052010-08-05Bibliographically approved