Discriminant varieties and discriminant ideals for operator vessels in Banach space
Copyright policy )Discriminant varieties and discriminant ideals for operator vessels in Banach space
A multivariate analogue of the theory of characteristic functions (for single linear operators) was advocated for several decades by M. S. Livšic and his school. In particular he has created the notion of a commutative operator vessel, which indeed encodes the expected features of a characteristic function for commutative \(n\)-tuples of Hilbert space operators with finite rank imaginary parts [see \textit{M. S. Livšic}, Integral Equations Oper. Theory 2, 25-47 (1979; Zbl 0407.35072)]. The paper under review contains a mild generalization of vessels to the case of Banach space operators and secondly, and more important, a discussion on the intimate relation between determinantal varieties of such objects, Bezoutians of finite systems of polynomials in several variables and rational curves in the affine complex space.
discriminant, commutative operator vessel, Varieties and morphisms, characteristic functions, Banach space operators, commutative \(n\)-tuples of Hilbert space operators, finite rank imaginary parts, Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc., Cayley-Hamilton theorem, Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions), Bezoutians, determinantal varieties
discriminant, commutative operator vessel, Varieties and morphisms, characteristic functions, Banach space operators, commutative \(n\)-tuples of Hilbert space operators, finite rank imaginary parts, Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc., Cayley-Hamilton theorem, Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions), Bezoutians, determinantal varieties
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