Reflexivity of spaces of weakly summable sequences.
We deal with the space of Λ-summable sequences from a locally convex space E, where Λ is a metrizable perfect sequence space. We give a characterization of the reflexivity of Λ(E) in terms of that of Λ and E and the AK property. In particular, we prove that if Λ is an echelon sequence space and E is a Fréchet space then Λ(E) is reflexive if and only if Λ and E are reflexive.