On the structure of variable exponent spaces

The first part of this paper surveys several results on the lattice structure of variable exponent Lebesgue function spaces (or Nakano spaces) Lp(⋅)(Ω). In the second part strictly singular and disjointly strictly singular operators between spaces Lp(⋅)(Ω) are studied. New results on the disjoint strict singularity of the inclusions Lp(⋅)(Ω)↪Lq(⋅)(Ω) are given.