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

Dmitry S. Kalyuzhny\uı-Verbovetzki\uı
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Abstract

We 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.

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Dmitry S. Kalyuzhny\uı-Verbovetzki\uı. 2004-12-08. On the {Bessmertny\uı} Class of Homogeneous Positive Holomorphic Functions on a Product of Matrix Halfplanes. https://arxiv.org/abs/math/0412164

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