Reflexivity of vector-valued Köthe–Orlicz sequence spaces

Abstract

Let E be a Banach space, λ a perfect sequence space, and M an Orlicz function. Denote by $lambda;{(E,;M)}_r$the space of all weakly (M, λ) -summable sequences from E that are the limit of their finite sections. In this paper, wedescribe the continuous linear functionals on $lambda;{(E,;M)}_r$in terms of strongly (N, $lambda^ast$ ) -summable sequences in the dual$E^ast$of E , and then we give a characterization of the reflexivity of λ (E, M) in terms of that of λ and of E and theAK-property.