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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability and almost periodicity of asymptotically dominated semigroups of positive operators


Authors: E. Yu. Emel'yanov, U. Kohler, F. Räbiger and M. P. H. Wolff
Journal: Proc. Amer. Math. Soc. 129 (2001), 2633-2642
MSC (2000): Primary 47D03, 47B65, 46B40, 46L99
Published electronically: February 15, 2001
MathSciNet review: 1838786
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Abstract:

We discuss conditions such that strong stability and strong asymptotic compactness of a (discrete or continuous) semiflow defined on a subset in the positive cone of an ordered Banach space is preserved under asymptotic domination. This is used to show that on a Banach lattice with order continuous norm strong stability and almost periodicity of a (discrete or strongly continuous) semigroup of positive operators is preserved under asymptotic domination.


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Additional Information

E. Yu. Emel'yanov
Affiliation: Sobolev Institute of Mathematics at Novosibirsk, Universitetskii pr.4, 630090 Novosibirsk, Russia
Email: emelanov@math.nsc.ru

U. Kohler
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Email: utko@michelangelo.mathematik.uni-tuebingen.de

F. Räbiger
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Email: frra@michelangelo.mathematik.uni-tuebingen.de

M. P. H. Wolff
Affiliation: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Email: manfred.wolff@uni-tuebingen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05835-X
PII: S 0002-9939(01)05835-X
Keywords: Stability, almost periodicity, semigroup representation, asymptotic domination, ordered Banach space
Received by editor(s): October 29, 1998
Received by editor(s) in revised form: January 7, 2000
Published electronically: February 15, 2001
Communicated by: Dale Alspach
Article copyright: © Copyright 2001 American Mathematical Society