Full paper in PDF:
$%R. Zaharopol, On invariant elements for positive operators, Rev. Mat. Univ. Complut. Madrid 10 (1997), no. 1, 85106.%$

On Invariant Elements for Positive Operators
Radu ZAHAROPOL
Department of Mathematical Sciences
Binghamton University (SUNY at Binghamton)
Binghamton, New York 13902-6000 USA

Received: July 14, 1995
 
ABSTRACT

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.

1991 Mathematics Subject Classification: 47A35, 47B65, 28D99.