In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting; that is why our approach is different. We do not use Banach limits and the invariant elements we come up with are much easier to describe than the ones constructed involving Banach limits.
@article{urn:eudml:doc:44243,
title = {On invariant elements for positive operators.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {10},
year = {1997},
pages = {85-106},
zbl = {0892.47036},
mrnumber = {MR1452565},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44243}
}
Zaharopol, R. On invariant elements for positive operators.. Revista Matemática de la Universidad Complutense de Madrid, Tome 10 (1997) pp. 85-106. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44243/