Discriminant varieties and discriminant ideals for operator vessels in Banach space
type: Item
instance of: scholarly article
title: Discriminant varieties and discriminant ideals for operator vessels in Banach space
zbMATH Open document ID: 0854.47007
DOI: 10.1007/BF01203917
author: Naftali Kravitsky
published in: Integral Equations and Operator Theory
publication date: 1997-01-05T00:00:00Z
review text: 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.
reviewed by: Mihai Putinar
Mathematics Subject Classification ID: 47A48
Mathematics Subject Classification ID: 14A10
Mathematics Subject Classification ID: 35R20
zbMATH DE Number: 838570
zbMATH Keywords: discriminant
zbMATH Keywords: Cayley-Hamilton theorem
zbMATH Keywords: characteristic functions
zbMATH Keywords: commutative operator vessel
zbMATH Keywords: commutative \(n\)-tuples of Hilbert space operators
zbMATH Keywords: finite rank imaginary parts
zbMATH Keywords: Banach space operators
zbMATH Keywords: determinantal varieties
zbMATH Keywords: Bezoutians
MaRDI profile type: Publication
cites work: Q5818478
cites work: Q4769140
cites work: Q5606150
cites work: On the discriminant function of two commuting nonselfadjoint operators
cites work: Regular colligations for several commuting operators in Banach space
cites work: Bezoutian operator vessels in Banach space
cites work: Q4754499
cites work: Operator waves in Hilbert space and related partial differential equations
full work available at URL: https://doi.org/10.1007/bf01203917
OpenAlex ID: W2091955121
description: scientific article; zbMATH DE number 838570