On the local spectral theory for positive and non-positive operators
type: Item
instance of: scholarly article
title: On the local spectral theory for positive and non-positive operators
zbMATH Open document ID: 0829.47001
DOI: 10.1016/0019-3577(91)90020-8
author: Peter Meyer-Nieberg
published in: Indagationes Mathematicae. New Series
publication date: 1992-09-27T00:00:00Z
review text: We discuss the local spectral behaviour of a continuous linear operator \(T\) defined on a Banach space by means of a system of \(T\)-invariant not necessarily closed subspaces. A similar description was given by the author for a positive linear operator \(T\) on a Banach lattice \(E\) with the aid of a chain of \(T\)-invariant order ideals. Here we give a slightly different definition and get a system of \(T\)-invariant subspaces which is maximal in some sense. It turns out that many of the results which are valid for positive operators on a Banach lattice hold also in similar forms in this general situation. But, of course, for positive operators there are a lot of additional informations. We apply this method to deduce some well-known results of the local spectral theory. Our method is elementary and uses only some simple facts about the theory of holomorphic vector valued functions, and we do not assume the operators to have the single valued extension property.
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47B65
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 57314
zbMATH Keywords: invariant subspaces
zbMATH Keywords: local spectral behaviour of a continuous linear operator
zbMATH Keywords: Banach lattice
zbMATH Keywords: single valued extension property
MaRDI profile type: Publication
full work available at URL: 0019-3577(91)90020-8
OpenAlex ID: W2013043652
cites work: Q5584224
cites work: Q3794755
cites work: A partial spectral reduction for positive linear operators
cites work: An interpolation result for the spectral radius
cites work: Q5613420
cites work: Q4049667
description: scientific article; zbMATH DE number 57314