Cayley-Hamilton theorem, vector bundles and divisors of commuting operators

DOI10.1007/BF01691898zbMath0515.47020WikidataQ57406935 ScholiaQ57406935MaRDI QIDQ1051881

M. S. Livshits

Publication date: 1983

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

characteristic determinantcommuting operators in Hilbert spacescomplete system of unitary invariantsdeterminantal curves and related vector bundlesdiscriminant polynomial

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Structure theory of linear operators (47A65) Groups and semigroups of linear operators, their generalizations and applications (47D99) Fiber spaces and bundles in algebraic topology (55R99)

Related Items (13)

Finite dimensional de Branges spaces on Riemann surfaces ⋮ Model representations of commutative systems of linear operators ⋮ Beurling-Lax type theorems and Cuntz relations ⋮ A behavioral interpretation of Livšic systems ⋮ de Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem ⋮ Commuting operators over Pontryagin spaces with applications to system theory ⋮ Multidimensional realisation theory and polynomial system solving ⋮ Complete description of determinantal representations of smooth irreducible curves ⋮ Solitonic combinations and commuting nonselfadjoint operators ⋮ Solitonic combinations, commuting nonselfadjoint operators, and applications ⋮ Zero-pole interpolation for meromorphic matrix functions on an algebraic curve and transfer functions of 2D systems ⋮ Elementary transformations of determinantal representations of algebraic curves ⋮ Self-adjoint determinantal representations of real plane curves

Cites Work

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• Regular colligations for several commuting operators in Banach space
• A method for constructing triangular canonical models of commuting operators based on connections with algebraic curves
• HOLOMORPHIC BUNDLES OVER ALGEBRAIC CURVES AND NON-LINEAR EQUATIONS
• LINE BUNDLES AND HOMOGENEOUS MATRICES

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