TY  - JOUR
A1  - Gerlach, Moritz Reinhardt
A1  - Glück, Jochen
T1  - Mean ergodicity vs weak almost periodicity
T2  - Studia mathematica
N2  - We provide explicit examples of positive and power-bounded operators on c(0) and l(infinity) which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature. Finally, we prove that if T is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of T .
KW  - positive operators
KW  - weakly almost periodic
KW  - order continuous norm
KW  - KB-space
KW  - mean ergodic
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/50723
SN  - 0039-3223
SN  - 1730-6337
VL  - 248
IS  - 1
SP  - 45
EP  - 56
PB  - Polska Akademia Nauk, Instytut Matematyczny
CY  - Warszawa
ER  -