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

Emel'Yanov E.

POSITIVITY, vol.1, no.4, pp.291-295, 1997 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 1 Issue: 4
  • Publication Date: 1997
  • Doi Number: 10.1023/a:1009764031312
  • Journal Name: POSITIVITY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.291-295
  • Keywords: Banach lattice, reflexive Banach lattice, countable order completeness, power-bounded operator, mean ergodic operator, regular operator
  • Middle East Technical University Affiliated: No

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.