Disjointly strictly singular inclusions between variable Lebesgue spaces

Disjointly strictly singular inclusions between variable Lebesgue spaces L^p () () 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 L^p () () L^q () () is not disjointly strictly singular. No restrictions on the exponent are imposed.