Matematičeskie trudy, Tome 2 (1999) no. 2, pp. 3-11
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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/
@article{MT_1999_2_2_a0,
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}},
journal = {Matemati\v{c}eskie trudy},
pages = {3--11},
year = {1999},
volume = {2},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MT_1999_2_2_a0/}
}
TY - JOUR
AU - S. G. Gorokhova
AU - È. Yu. Emel'yanov
TI - A Sufficient Condition for Order Boundedness of an Attractor for a Positive Mean Ergodic Operator in a Banach Lattice
JO - Matematičeskie trudy
PY - 1999
SP - 3
EP - 11
VL - 2
IS - 2
UR - http://geodesic.mathdoc.fr/item/MT_1999_2_2_a0/
LA - ru
ID - MT_1999_2_2_a0
ER -
%0 Journal Article
%A S. G. Gorokhova
%A È. Yu. Emel'yanov
%T A Sufficient Condition for Order Boundedness of an Attractor for a Positive Mean Ergodic Operator in a Banach Lattice
%J Matematičeskie trudy
%D 1999
%P 3-11
%V 2
%N 2
%U http://geodesic.mathdoc.fr/item/MT_1999_2_2_a0/
%G ru
%F MT_1999_2_2_a0
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].
