lq-structure of variable exponent spaces

It is shown that a separable variable exponent (or Nakano) function space Lp(⋅)(Ω) has a lattice-isomorphic copy of lq if and only if q∈Rp(⋅), the essential range set of the exponent function p(⋅). Consequently Rp(⋅) is a lattice-isomorphic invariant set. The values of q such that lq embeds isomorphically in Lp(⋅)(Ω) is determined. It is also proved the existence of a bounded orthogonal lq-projection in the space Lp(⋅)(Ω), for every q∈Rp(⋅).