Generic existence and uniqueness of positive eigenvalues and eigenvectors

Authors
Reich, S Zaslavski, AJ
Citation
S. Reich et Aj. Zaslavski, Generic existence and uniqueness of positive eigenvalues and eigenvectors, INTEG EQ OP, 41(4), 2001, pp. 455-471
Citations number
12
Categorie Soggetti
Mathematics
Journal title
INTEGRAL EQUATIONS AND OPERATOR THEORY
ISSN journal
0378620X → ACNP
Volume
41
Issue
4
Year of publication
2001
Pages
455 - 471
Database
ISI
SICI code
0378-620X(200112)41:4<455:GEAUOP>2.0.ZU;2-W
Abstract
We consider a closed cone of positive operators on an ordered Banach space and prove that a generic element of this cone has a unique positive eigenva lue and a unique (up to a positive multiple) positive eigenvector. Moreover , the normalized iterations of such a generic element converge to its uniqu e eigenvector.