Positive Operators on Banach Spaces Ordered by Strongly Normal Cones

Positive Operators on Banach Spaces Ordered by Strongly Normal Cones Positivity 7: 3–22, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. Positive Operators on Banach Spaces Ordered by Strongly Normal Cones EDUARD YU. EMEL’YANOV and MANFRED P. H. WOLFF Universität Tübingen, Wilhelmstrasse 7, D-72074 Tübingen, Germany Mathematics Subject Classification 2000: Primary 47B60, Secondary: 47A35, 47C15, 46B40 Key words: positive operators, mean ergodic operators, asymptotic domination 1. Introduction In [13] we have introduced the class of ideally ordered Banach spaces. This class includes all Banach lattices with order continuous norm as well as the predual of any von Neumann algebra. We have shown in [13] that semigroups of positive operators on ideally ordered Banach spaces possess specific asymptotic properties. In this paper we continue these investigations and apply our technique to positive semigroups with small attractors thus generalizing the main results of [11, 12], which were stated there for Markov semigroups only. We do not restrict ourselves to ideally ordered Banach spaces but study in more details Banach spaces ordered by a strongly normal cone, which includes all Banach lattices as well as all C - algebras. Many results presented here were known before only for Banach lattices. For simplicity, we deal with single operators, however all results http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Positive Operators on Banach Spaces Ordered by Strongly Normal Cones

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2003 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1025807816198
Publisher site
See Article on Publisher Site

Abstract

Positivity 7: 3–22, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands. Positive Operators on Banach Spaces Ordered by Strongly Normal Cones EDUARD YU. EMEL’YANOV and MANFRED P. H. WOLFF Universität Tübingen, Wilhelmstrasse 7, D-72074 Tübingen, Germany Mathematics Subject Classification 2000: Primary 47B60, Secondary: 47A35, 47C15, 46B40 Key words: positive operators, mean ergodic operators, asymptotic domination 1. Introduction In [13] we have introduced the class of ideally ordered Banach spaces. This class includes all Banach lattices with order continuous norm as well as the predual of any von Neumann algebra. We have shown in [13] that semigroups of positive operators on ideally ordered Banach spaces possess specific asymptotic properties. In this paper we continue these investigations and apply our technique to positive semigroups with small attractors thus generalizing the main results of [11, 12], which were stated there for Markov semigroups only. We do not restrict ourselves to ideally ordered Banach spaces but study in more details Banach spaces ordered by a strongly normal cone, which includes all Banach lattices as well as all C - algebras. Many results presented here were known before only for Banach lattices. For simplicity, we deal with single operators, however all results

Journal

PositivitySpringer Journals

Published: Oct 17, 2004

References

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