The positive fixed points of Banach lattices

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Abstract

Let Z be a Banach lattice endowed with positive cone C and an order-continuous norm j.j . Let G be a left-amenable semigroup of positive linear endomorphisms of Z . Then the positive fixed points Co of Z under G form a lattice cone, and their linear span Z0 is a Banach lattice under an order-continuous norm ||.||0 which agrees with |.| on Co. A counterexample shows that under the given conditions Z0 need not contain all the fixed points of Z under G , and need not be a sublattice of (Z, C). The paper concludes with a discussion of some related results.
Original languageEnglish
Pages (from-to)255-260
JournalProceedings of the American Mathematical Society
Volume107
Issue number1
Publication statusPublished - 1989

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