Carathéodory interpolation on the non-commutative polydisk

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dc.creatorKalyuzhny\uı-Verbovetzki\uı, Dmitry S.
dc.date2004-12-08
dc.date2005-03-17
dc.date.accessioned2026-07-07T05:15:05Z
dc.date.available2026-07-07T05:15:05Z
dc.descriptionThe Carathéodory problem in the $N$-variable non-commutative Herglotz--Agler class and the Carathéodory--Fejér problem in the $N$-variable non-commutative Schur--Agler class are posed. It is shown that the Carathéodory (resp., Carathéodory--Fejér) problem has a solution if and only if the non-commutative polynomial with given operator coefficients (the data of the problem indexed by an admissible set $Λ$) takes operator values with positive semidefinite real part (resp., contractive operator values) on $N$-tuples of $Λ$-jointly nilpotent contractive $n\times n$ matrices, for all $n\in\mathbb{N}$.
dc.descriptionto appear in J. Funct. Anal
dc.identifierhttps://arxiv.org/abs/math/0412161
dc.identifierhttp://arxiv.org/abs/math/0412161
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73519
dc.subjectFunctional Analysis
dc.subject47A57; 47A13; 46L89; 47A20
dc.titleCarathéodory interpolation on the non-commutative polydisk
dc.typetext

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