Applications of the Birkhoff-Hopf Theorem to the spectral theory of positive linear operators

Simon Eveson; Roger Nussbaum

doi:10.1017/S0305004100073321

Applications of the Birkhoff-Hopf Theorem to the spectral theory of positive linear operators

Simon Eveson, Roger Nussbaum

Mathematics

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Abstract

This paper may be regarded as a sequel to our earlier paper [19], where we give an elementary and self-contained proof of a very general form of the Hopf theorem on order-preserving linear operators in partially ordered vector spaces (reproduced here as Theorem 1·1).
Versions of this theorem and related ideas have been used by various authors to study both linear and nonlinear integral equations (Thompson [41], Bushell [9, 11], Potter [38, 39], Eveson [16, 17], Bushell and Okrasiriski [12, 13]); the convergence properties of nonlinear maps (Nussbaum [32, 33]); so-called DAD theorems (Borwein, Lewis and Nussbaum [8]) and in the proof of weak ergodic theorems (Fujimoto and Krause [20], Nussbaum [34]).

Original language	English
Pages (from-to)	491-512
Number of pages	22
Journal	Math Proc Camb Phil Soc
Volume	117
Issue number	3
DOIs	https://doi.org/10.1017/S0305004100073321
Publication status	Published - 1995

Keywords

Analysis

Access to Document

10.1017/S0305004100073321

Cite this

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title = "Applications of the Birkhoff-Hopf Theorem to the spectral theory of positive linear operators",

abstract = "This paper may be regarded as a sequel to our earlier paper [19], where we give an elementary and self-contained proof of a very general form of the Hopf theorem on order-preserving linear operators in partially ordered vector spaces (reproduced here as Theorem 1·1). Versions of this theorem and related ideas have been used by various authors to study both linear and nonlinear integral equations (Thompson [41], Bushell [9, 11], Potter [38, 39], Eveson [16, 17], Bushell and Okrasiriski [12, 13]); the convergence properties of nonlinear maps (Nussbaum [32, 33]); so-called DAD theorems (Borwein, Lewis and Nussbaum [8]) and in the proof of weak ergodic theorems (Fujimoto and Krause [20], Nussbaum [34]). ",

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T1 - Applications of the Birkhoff-Hopf Theorem to the spectral theory of positive linear operators

AU - Eveson, Simon

AU - Nussbaum, Roger

PY - 1995

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AB - This paper may be regarded as a sequel to our earlier paper [19], where we give an elementary and self-contained proof of a very general form of the Hopf theorem on order-preserving linear operators in partially ordered vector spaces (reproduced here as Theorem 1·1). Versions of this theorem and related ideas have been used by various authors to study both linear and nonlinear integral equations (Thompson [41], Bushell [9, 11], Potter [38, 39], Eveson [16, 17], Bushell and Okrasiriski [12, 13]); the convergence properties of nonlinear maps (Nussbaum [32, 33]); so-called DAD theorems (Borwein, Lewis and Nussbaum [8]) and in the proof of weak ergodic theorems (Fujimoto and Krause [20], Nussbaum [34]).

KW - Analysis

U2 - 10.1017/S0305004100073321

DO - 10.1017/S0305004100073321

M3 - Article

VL - 117

SP - 491

EP - 512

JO - Math Proc Camb Phil Soc

JF - Math Proc Camb Phil Soc

IS - 3

ER -