Property ββ of Rolewicz and orthogonal convexities of Calderón–Lozanovskiĭ spaces

We find criteria for property ββ of Rolewicz and orthogonal convexities in Calderón–Lozanovskiĭ spaces. In order to present characterization for property ββ in the sequence case, we introduce a new respective monotonicity property. The particular case of Orlicz–Lorentz spaces will also be discussed.