Dmitry S. Kalyuzhnyui-Verbovetzkiui

collaborators

4 papers

math.FA2004

Non-commutative positive kernels and their matrix evaluations

Dmitry S. Kalyuzhny\uı-Verbovetzki\uı, Victor Vinnikov

We show that a formal power series in $2 N$ non-commuting indeterminates is a positive non-commutative kernel if and only if the kernel on $N$ -tuples of matrices of any size obtaine…

math.FA2004

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

Dmitry S. Kalyuzhny\uı-Verbovetzki\uı

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…

math.FA2004

Multivariable $ρ$ -contractions

Dmitry S. Kalyuzhny\uı-Verbovetzki\uı

We suggest a new version of the notion of $ρ$ -dilation ( $ρ > 0$ ) of an $N$ -tuple $A = (A_{1}, ..., A_{N})$ of bounded linear operators on a common Hilbert space. We say that $\mathb…

math.FA2004

Carathéodory interpolation on the non-commutative polydisk

Dmitry S. Kalyuzhny\uı-Verbovetzki\uı

The 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 po…

Non-commutative positive kernels and their matrix evaluations

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

Multivariable ρ-contractions

Carathéodory interpolation on the non-commutative polydisk

Multivariable $ρ$ -contractions