Banach lattices on which every power-bounded operator is mean ergodic

Date

1997-01-01

Author

Emelyanov, Eduard

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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.

Subject Keywords

Banach lattice, reflexive Banach lattice, countable order completeness, power-bounded operator, mean ergodic operator, regular operator

URI

https://hdl.handle.net/11511/94700

Journal

POSITIVITY

DOI

https://doi.org/10.1023/a:1009764031312

Collections

Department of Mathematics, Article

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Citation Formats

E. Emelyanov, “Banach lattices on which every power-bounded operator is mean ergodic,” POSITIVITY, vol. 1, no. 4, pp. 291–295, 1997, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/94700.