Some topological properties of double Ces aro-Orlicz sequence spaces

Abstract

The object of this paper is to introduce the double Cesàro-Orlicz sequence space Ces (2) M using a Orlicz function M. Necessary and sufficient conditions under which the double Cesàro-Orlicz sequence space Ces (2) M is nontrivial are presented. It is proved that double Cesàro-Orlicz sequence spaces Ces (2) M are complete. Finally, it is obtained that if φ ∈ ∆ 2 (0) then the space Ces (2) M is separable and order continuous.