Asymptotic Behavior of Positive Operators on Banach Lattices

Asymptotic Behavior of Positive Operators on Banach Lattices Positivity 4: 245–251, 2000. © 2000 Kluwer Academic Publishers. Printed in the Netherlands. Asymptotic Behavior of Positive Operators on Banach Lattices 1 2 3 E.YU. EMEL’YANOV , F. RÄBIGER and M.P.H. WOLFF Sobolev Institute of Mathematics at NBovosibirsk, Universitetskii pr. 4, 630090 Novosibirsk, Russia E-mail: Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany E-mail: E-mail: 1. Introduction In the present paper we present some results dealing with the asymptotic behavior of positive operators on a Banach lattice. Some of the results are known. The others were recently obtained by the authors. We will consider mean ergodicity, strong stability, and almost periodicity of positive operators directly and in connection with some properties of the Banach lattice on which they act. Several results require countable order completeness or the existence of a topological orthogonal system in the Banach lattice which is satisfied for all classical Banach lattices. This leads to some open questions which will be posed in the paper. Our terminology and notations are standard and follow to books of [5, 7] and [13]. We consider bounded linear operators on complex Banach spaces and Banach lattices. 1. Let X be a Banach space. An Positivity Springer Journals

Asymptotic Behavior of Positive Operators on Banach Lattices

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Kluwer Academic Publishers
Copyright © 2000 by Kluwer Academic Publishers
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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  • Banach lattices on which every power-bounded operator is mean ergodic
    Emel'yanov, E. Y.

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