The positive fixed points of Banach lattices
Christianson, B.
(1989)
The positive fixed points of Banach lattices.
Proceedings of the American Mathematical Society, 107 (1).
pp. 255-260.
ISSN 0002-9939
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.
Item Type | Article |
---|---|
Additional information | Original article can be found at: http://www.ams.org/publications/journals/journalsframework/proc Copyright AMS. |
Date Deposited | 15 May 2025 11:38 |
Last Modified | 30 May 2025 23:34 |
-
picture_as_pdf - 903929.pdf
Share this file
Downloads