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Banach lattices on which every power-bounded operator is mean ergodic
Date
1997-01-01
Author
Emelyanov, Eduard
Metadata
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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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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.