Geodesic
A Sufficient Condition for Order Boundedness of an Attractor for a Positive Mean Ergodic Operator in a Banach Lattice
Matematičeskie trudy, Tome 2 (1999) no. 2, pp. 3-11 Cet article a éte moissonné depuis la source Math-Net.Ru

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We establish that a positive mean ergodic operator with a quasi-order-bounded attractor on a Banach lattice has an order-bounded attractor. This generalizes the recent result of F. Räbiger [1, Main Lemma 3.3] that was proven under the additional assumption that the operator in question is contractive. As an application, several theorems are established which generalize some results of [1–3]. 
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     author = {S. G. Gorokhova and \`E. Yu. Emel'yanov},
     title = {A {Sufficient} {Condition} for {Order} {Boundedness} of {an~Attractor} for {a~Positive} {Mean} {Ergodic} {Operator} in {a~Banach} {Lattice}},
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S. G. Gorokhova; È. Yu. Emel'yanov. A Sufficient Condition for Order Boundedness of an Attractor for a Positive Mean Ergodic Operator in a Banach Lattice. Matematičeskie trudy, Tome 2 (1999) no. 2, pp. 3-11. http://geodesic.mathdoc.fr/item/MT_1999_2_2_a0/