Convexity characteristic of Calderón–Lozanovskiĭ sequence spaces

Hudzik, Kamińska and Masty?o obtained some geometric properties of Calderón–Lozanovski? function spaces which are defined on a nonatomic σ‐measure space in Houston. J. Math. 22 (1996), but left the case of atomic measure unsolved. We studied the relevant problems for the sequence spaces and obtained the following main results:

, is order continuous if and only if and e is order continuous.
1. Let Φ be strictly convex on , then the convex characteristic whenever e is not order continuous or ; if e is uniformly monotone and , then .
2. For the Orlicz‐Lorentz sequence space , if or , or ω is not regular; if Φ is strictly convex on , and ω is regular.