2006/07/28 by Cui, Yunan, Hudzik, Henryk, Petrot, Narin +2
#46B20 #46B45 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.math/0607730
Necessary and sufficient conditions under which the Cesàro--Orlicz sequence space \cfi is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro--Orlicz spaces \cfi have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in \cfi can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces \cfi are given.