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Banach Lattices on Which Every Power-Bounded Operator is Mean Ergodic

Banach Lattices on Which Every Power-Bounded Operator is Mean Ergodic Given a Banach lattice E that fails to be countably order complete, we construct a positive compact operator A: E → E for which T = I - A is power-bounded and not mean ergodic. As a consequence, by using the theorem of R. Zaharopol, we obtain that if every power-bounded operator in a Banach lattice is mean ergodic then the Banach lattice is reflexive. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Banach Lattices on Which Every Power-Bounded Operator is Mean Ergodic

Positivity , Volume 1 (4) – Oct 14, 2004

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References (5)

Publisher
Springer Journals
Copyright
Copyright © 1997 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
DOI
10.1023/A:1009764031312
Publisher site
See Article on Publisher Site

Abstract

Given a Banach lattice E that fails to be countably order complete, we construct a positive compact operator A: E → E for which T = I - A is power-bounded and not mean ergodic. As a consequence, by using the theorem of R. Zaharopol, we obtain that if every power-bounded operator in a Banach lattice is mean ergodic then the Banach lattice is reflexive.

Journal

PositivitySpringer Journals

Published: Oct 14, 2004

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