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An elementary proof of the Birkhoff-Hopf Theorem

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JournalMathematical Proceedings of the Cambridge Philosophical Society
DatePublished - Jan 1995
Issue number1
Number of pages25
Pages (from-to)31-55
Original languageEnglish


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...

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