Generalized Köthe-Toeplitz Duals of Some Vector-Valued Sequence Spaces

Abstract EN

We know from the classical sequence spaces theory that there is a useful relationship between continuous and β-duals of a scalar-valued FK-space E originated by the AK-property.

Our main interest in this work is to expose relationships between the operator space ℒ(E,Y) and Eβ and the generalized β-duals of some X-valued AK-space E where X and Y are Banach spaces and Eβ={(Ak),Ak∈ℒ(X,Y):∑k=1∞Akxk converges in Y,for all x∈E}.

Further, by these results, we obtain the generalized β-duals of some vector-valued Orlicz sequence spaces.