An elementary proof of the Birkhoff-Hopf Theorem

S P Eveson; R D Nussbaum

doi:10.1017/S0305004100072911

An elementary proof of the Birkhoff-Hopf Theorem

S P Eveson, R D Nussbaum

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In important work some thirty years ago, G. Birkhoff[2, 3] and E. Hopf [16, 17] showed that large classes of positive linear operators behave like contraction mappings with respect to certain ‘almost’ metrics. Hopf worked in a space of measurable functions and took as his ‘almost’ metric the oscillation ¿(y/x) of functions y and x with x(t) > 0 almost everywhere, defined by...

Original language	English
Pages (from-to)	31-55
Number of pages	25
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	117
Issue number	1
DOIs	https://doi.org/10.1017/S0305004100072911
Publication status	Published - Jan 1995

Keywords

ERGODIC-THEOREMS
OPERATORS

Access to Document

10.1017/S0305004100072911

Cite this

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abstract = "In important work some thirty years ago, G. Birkhoff[2, 3] and E. Hopf [16, 17] showed that large classes of positive linear operators behave like contraction mappings with respect to certain {\textquoteleft}almost{\textquoteright} metrics. Hopf worked in a space of measurable functions and took as his {\textquoteleft}almost{\textquoteright} metric the oscillation ¿(y/x) of functions y and x with x(t) > 0 almost everywhere, defined by... ",

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