The positive fixed points of Banach lattices
Christianson, B.
(1989)
The positive fixed points of Banach lattices.
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 |
---|---|
Date Deposited | 26 Jul 2024 20:52 |
Last Modified | 26 Jul 2024 20:53 |
Downloads
Share this file
Explore Further
Read more research from the creator(s):
Find work associated with the faculties and division(s):