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

Emel'Yanov, EDUARD

doi:10.1023/a:1009764031312

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

Emel'Yanov E.

POSITIVITY, cilt.1, sa.4, ss.291-295, 1997 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 1 Sayı: 4
Basım Tarihi: 1997
Doi Numarası: 10.1023/a:1009764031312
Dergi Adı: POSITIVITY
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Sayfa Sayıları: ss.291-295
Anahtar Kelimeler: Banach lattice, reflexive Banach lattice, countable order completeness, power-bounded operator, mean ergodic operator, regular operator
Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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.