The joint characteristic function of a commutative operator vessel in Banach space
type: Item
instance of: scholarly article
title: The joint characteristic function of a commutative operator vessel in Banach space
zbMATH Open document ID: 0867.47011
DOI: 10.1007/BF01308630
author: Naftali Kravitsky
published in: Integral Equations and Operator Theory
publication date: 1996-07-23T00:00:00Z
review text: The characteristic function of a single operator, a basic object of study in modern operator theory, was generalized by M. S. Livsic to a class of pairs of commuting linear operators. There exists at present a well developed theory of joint characteristic functions, with application to operator theory, algebraic geometry and systems theory, see \textit{N. Kravitsky}, \textit{M. S. Livsic}, \textit{A. Markus} and \textit{V. Vinnikov}, ``Theory of commuting non-selfadjoint operators'' (1995; Zbl 0834.47004). The paper deals with \(n\)-tuples of commuting operators in Banach space, with \(n>2\). The programme of regarding the joint characteristic function as a morphism of vector bundles, carried by the discriminant variety of the system is developed in analogy with the known case of commuting pairs of operators.
reviewed by: Mihai Putinar
Mathematics Subject Classification ID: 47A48
Mathematics Subject Classification ID: 47A13
zbMATH DE Number: 908005
zbMATH Keywords: joint characteristic functions
zbMATH Keywords: \(n\)-tuples of commuting operators
zbMATH Keywords: morphism of vector bundles
MaRDI profile type: Publication
cites work: Q5606150
cites work: Bezoutian operator vessels in Banach space
cites work: Discriminant varieties and discriminant ideals for operator vessels in Banach space
cites work: Q4317795
cites work: Q3326298
description: scientific article; zbMATH DE number 908005