Disjoint strict singularity of inclusions between rearrangement invariant spaces (Q2717557)

The authors consider rearrangement invariant (r.i.) function spaces on the interval \([0,\infty)\). The main results of this paper are concerned with the disjoint strict singularity (DSS) of the inclusion operator between arbitrary r.i. spaces on the interval \([0,\infty)\). Very important are conditions when the inclusion operator \(L^1\cap L^\infty\hookrightarrow E\) is DSS or is strictly singular or is weakly compact, and moreover when the inclusion operator \(E\hookrightarrow L^1\cap L^\infty\) is DSS. This interesting paper contains also some important applications to the classes of Lorentz and Marcinkiewicz spaces.