Non-commutative positive kernels and their matrix evaluations

DOI10.1090/S0002-9939-05-08127-XzbMath1092.47013arXivmath/0412165MaRDI QIDQ5713201

Dmitry S. Kaliuzhnyi-Verbovetzkyi, Victor Vinnikov

Publication date: 12 December 2005

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0412165

zbMATH Keywords

factorizationformal power serieshereditary polynomialsmatrix substitutionsnon-commuting indeterminatespositive non-commuting kernels

Mathematics Subject Classification ID

Functional calculus for linear operators (47A60) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Formal power series rings (13F25)

Related Items (6)

Non-commutative varieties with curvature having bounded signature ⋮ Tensorial function theory: from Berezin transforms to Taylor's Taylor series and back ⋮ Noncommutative reproducing kernel Hilbert spaces ⋮ Noncommutative ball maps ⋮ Classification of all noncommutative polynomials whose Hessian has negative signature one and a noncommutative second fundamental form ⋮ Carathéodory interpolation on the non-commutative polydisk

Cites Work

• On the intersection of null spaces for matrix substitutions in a non-commutative rational formal power series
• Schur functions, operator colligations, and reproducing kernel Pontryagin spaces
• ``Positive noncommutative polynomials are sums of squares.
• A non-commutative Positivstellensatz on isometries
• Theory of Reproducing Kernels
• Factorization of operator-valued polynomials in several non-commuting variables
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