Strictly singular and disjointly strictly singular inclusions

The Strictly Singular (SS) and Disjointly Strictly Singular (DSS) r.i. space inclusions in a Banach Space are studied. The study results show that the for a pair of r.i. spaces with one of the spaces being separable, the inclusions are SS, and the inclusions are DSS and the norms of the inclusions are not equivalent. The inclusion of Oelicz space is not SS if the infinite limit of an inferior positive convex function is greater than 4 and the supreme positive convex function is less than 4. The results also show that the inclusions is SS if and only if the zero limit of the concave increasing function is equal to zero. Any subspace on which the norms of equivalent Orlicz spaces are defined, the space is uncomplemented.