Commutant lifting for commuting row contractions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 22 Mar 2010Embargo end date: 01 Jan 2009 English Publisher:WileyJournal:Bulletin of the London Mathematical Society, volume 42, pages 506-516 (issn: 0024-6093,

Copyright policy )Funded by:NSERC | unidentified

Authors: Davidson, Kenneth R.; Le, Trieu;

doi: 10.1112/blms/bdq016 , 10.48550/arxiv.0906.4526

arXiv: 0906.4526

Commutant lifting for commuting row contractions

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Abstract

If $T= \big[ T_1 ... T_n\big]$ is a row contraction with commuting entries, and the Arveson dilation is $\tilde T= \big[ \tilde T_1 ... \tilde T_n\big]$, then any operator $X$ commuting with each $T_i$ dilates to an operator $Z$ of the same norm which commutes with each $\tilde T_i$.

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Keywords

Mathematics - Functional Analysis, Mathematics - Operator Algebras, FOS: Mathematics, 47A20, Operator Algebras (math.OA), Functional Analysis (math.FA)

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