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Applications of the Birkhoff–Hopf theorem to the spectral theory of positive linear operators

Published online by Cambridge University Press:  24 October 2008

Simon P. Eveson  and
Roger D. Nussbaum
Simon P. Eveson
Affiliation:
Department of Mathematics, University of York, Heslington, York YO1 5DD
Roger D. Nussbaum
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey, U.S.A.08904
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Extract

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]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 117 , Issue 3 , May 1995 , pp. 491 - 512
Copyright
Copyright © Cambridge Philosophical Society 1995

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