Köthe Dual of Some Vector-valued Sequence Spaces

We study some properties of the spaces λ(E) of weakly λ-summable sequences and λ⟨E⟩ of strongly λ-summable sequences of a locally convex space E. For example, after proving results on bounded sets of these spaces, we express the elements of their K öthe duals in terms of sequences in the continuous dual E′ of E, then we prove that these spaces possess the AK property if and only if the K ̈othe dual coincides with the continuous dual.