Disjointly strictly singular and L-weakly compact inclusions between variable Lebesgue spaces

Abstract

Disjointly strictly singular inclusions between variable Lebesgue spaces Lp(·)(μ) on finite measure are characterized. Suitable criteria in terms of the (bounded or unbounded) exponents are given. It is proved the equivalence of L-weak compactness (also called almost compactness) and disjoint strict singularity for variable Lebesgue space inclusions. For infinite measure any inclusion Lp(·)(μ) → Lq(·)(μ) is not disjointly strictly singular. No restrictions on the exponent are imposed.