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Matematicheskie Trudy, 1999, Volume 2, Number 2, Pages 3–11 (Mi mt151)  
This article is cited in 4 scientific papers (total in 4 papers)

A Sufficient Condition for Order Boundedness of an Attractor for a Positive Mean Ergodic Operator in a Banach Lattice

S. G. Gorokhovaa, È. Yu. Emel'yanovb

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (245 kB) Citations (4)
Abstract: 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].
Key words: Banach lattice, KB-space, contractive operator, attractor for an operator, positive mean ergodic operator, asymptotically periodic operator.
Received: 30.11.1998
Bibliographic databases:
UDC: 517.95
Language: Russian
Citation: 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”, Mat. Tr., 2:2 (1999), 3–11; Siberian Adv. Math., 9:3 (1999), 78–85
Citation in format AMSBIB
\Bibitem{GorEme99}
\by S.~G.~Gorokhova, \`E.~Yu.~Emel'yanov
\paper A Sufficient Condition for Order Boundedness of an~Attractor for a~Positive Mean Ergodic Operator in a~Banach Lattice
\jour Mat. Tr.
\yr 1999
\vol 2
\issue 2
\pages 3--11
\mathnet{http://mi.mathnet.ru/mt151}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1767821}
\zmath{https://zbmath.org/?q=an:0944.47022}
\transl
\jour Siberian Adv. Math.
\yr 1999
\vol 9
\issue 3
\pages 78--85
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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