POSITIVITY, vol.1, no.4, pp.291-295, 1997 (Journal Indexed in SCI)
Article / Article
Title of Journal :
Banach lattice, reflexive Banach lattice, countable order completeness, power-bounded operator, mean ergodic operator, regular operator
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.