Generalized Köthe-Toeplitz duals of some vector-valued sequence spaces (Q355617)

Summary: We know from the classical sequence space theory that there is a useful relationship between continuous and \(\beta\)-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 \(\mathcal L(E, Y)\) and \(E^\beta\) and the generalized \(\beta\)-duals of some \(X\)-valued AK-space \(E\), where \(X\) and \(Y\) are Banach spaces and \(E^\beta = \{(A_k): A_k \in \mathcal L(X, Y)\), \(\sum^\infty_{k=1} A_kx_k\) converges in \(Y\) for all \(x \in E\}\). Further, by these results, we obtain the generalized \(\beta\)-duals of some vector-valued Orlicz sequence spaces.