Positive operators on Banach spaces ordered by strongly normal cones (Q1412286)

The authors study some properties of positive operators on ideally ordered Banach spaces and Banach spaces ordered by strongly normal cones. They obtain several sufficient conditions under which a positive operator is mean ergodic, almost periodic or constrictive. The theorems presented in the paper under review generalize earlier results for Banach lattices (see, for example, Theorem 6). It is mentioned that the problem whether every normal cone is strongly normal is still open.