l(q)-structure of variable exponent spaces

Abstract

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