Rational operator functions and Bezoutian operator vessels
type: Item
instance of: scholarly article
title: Rational operator functions and Bezoutian operator vessels
zbMATH Open document ID: 0943.47010
DOI: 10.1007/BF01229505
author: Naftali Kravitsky
published in: Integral Equations and Operator Theory
publication date: 2000-08-28T00:00:00Z
review text: In previous work the author has developed a theory of operator vessels associated with operators \(A_1,A_2,\dots, A_n,B_1,B_2,\dots,B_n\) on a Banach space such that the differences \(A_j-B_j\) are small (e.g., of finite rank). A special kind of vessel can be constructed when the operators \(A_j,B_j\) are obtained as rational functions of operators \(A, B\) (i.e., \(A_j=r_j(A)\) and \(B_j=r_j(B))\) with rank one difference \(A-B\). The author makes a general conjecture about sufficient conditions under which a given vessel can be identified with one of the special kind. He proves this conjecture for \(n=2\).
reviewed by: H. Bercovici
Mathematics Subject Classification ID: 47A48
Mathematics Subject Classification ID: 14E05
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 47B49
Mathematics Subject Classification ID: 47A60
zbMATH DE Number: 938767
zbMATH Keywords: operator colligations
zbMATH Keywords: operator vessels
zbMATH Keywords: Livsic characteristic function
zbMATH Keywords: invariant subspaces
zbMATH Keywords: rational functions of operators
MaRDI profile type: Publication
cites work: Q5606150
cites work: Regular colligations for several commuting operators in Banach space
cites work: Bezoutian operator vessels in Banach space
cites work: Discriminant varieties and discriminant ideals for operator vessels in Banach space
cites work: The joint characteristic function of a commutative operator vessel in Banach space
cites work: On some resultant identities
description: scientific article; zbMATH DE number 938767