On invariant elements for positive operators

Abstract

In tbe paper we atud>’ the existence of nonzero positive invaruant elementa for positivo operatora in Riesz apeen. The cinas of Riesz apaces for which the results are valid fr large enough to contain ah the Banachlattices with arder continuous norma. Ah the resulta obtained in earhier works deal with positive operators in KB-spaces aud iii many of them the approach ja based upan tite use of Banach llinita. The metitoda created for KB-spaces cannot be extended to oir more general setting; tbat is why oir approacb la different. We do not use Banach limita aud tbe invariant elementa we come up with are much ensier to describe than tbe ones constructed involving Banach limita.