Some properties of Jordan sets of vectors of linear operators in Banach spaces
type: Item
instance of: scholarly article
title: Some properties of Jordan sets of vectors of linear operators in Banach spaces
zbMATH Open document ID: 1264.47002
author: Mikhail Arkad'evich Elishevich
publication date: 2012-09-05T00:00:00Z
review text: Let \(E_1,E_2\) be reflexive Banach spaces, \(A,B\:E_1\to E_2\) be linear and closed operators with \(D(A)=D(B)=E_1\), \(\dim\ker A\neq0\) and/or \(\dim\ker B\neq0\). The authors prove: (1)~If there exist \(r\geq 0\) finite Jordan chains of vectors for \(B\) with respect to \(A\), then there exist \(r\) finite Jordan chains of functionals for the adjoint operator \(B^*\) with respect to~\(A^*\), having the same length; (2)~if there exist \(r\geq 0\) cyclic Jordan chains of functionals for \(B^*\) with respect to \(A^*\), then there exist \(r\) auxiliary chains of vectors for \(B\) with respect to~\(A\).
reviewed by: Zoran Kadelburg
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 6077047
zbMATH Keywords: Banach space
zbMATH Keywords: linear operator
zbMATH Keywords: vector functional
zbMATH Keywords: Jordan chain
MaRDI profile type: Publication
published in: The Bulletin of Irkutsk State University. Series Mathematics
description: scientific article; zbMATH DE number 6077047