On the {Bessmertny\uı} Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfplanes

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dc.creatorKalyuzhny\uı-Verbovetzki\uı, Dmitry S.
dc.date2004-12-08
dc.date.accessioned2026-07-07T05:15:05Z
dc.date.available2026-07-07T05:15:05Z
dc.descriptionWe generalize our earlier results from \cite{K} on the Bessmertny\uı class of operator-valued functions holomorphic in the open right poly-halfplane which admit representation as a Schur complement of a block of a linear homogeneous operator-valued function with positive semidefinite operator coefficients, to the case of a product of open right matrix halfplanes. Several equivalent characterizations of this generalized Bessmertny\uı class are presented. In particular, its intimate connection with the Agler--Schur class of holomorphic contractive operator-valued functions on the product of matrix unit disks is established.
dc.identifierhttps://arxiv.org/abs/math/0412164
dc.identifierhttp://arxiv.org/abs/math/0412164
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73522
dc.subjectFunctional Analysis
dc.subject47A48; 32A10; 47A56; 47A60
dc.titleOn the {Bessmertny\uı} Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfplanes
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