Yunan Cui, Henryk Hudzik, Narin Petrot, Suthep Suantai, Alicja Szymaszkiewicz
Published 2006-07-28Version 1
Necessary and sufficient conditions under which the Ces\`{a}ro--Orlicz sequence space $\cfi$ is nontrivial are presented. It is proved that for the Luxemburg norm, Ces\`{a}ro--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.
Köthe-Bochner spaces and some geometric properties related to rotundity and smoothness
On Geometric properties of Henstock-Orlicz spaces
On uniform Bishop-Phelps-Bollobás type approximations of linear operators and preservation of geometric properties
![QR code for arXiv:math/0607730 [math.FA]](http://oss.arxitics.com/images/favicon.svg)