Kothe-Toeplitz and Topological Duals of Spaces of Strongly Summable Vector Sequences

Abstract

We characterize generalized α-, β- and γ-duals of the spaces of strongly summable vector sequences l{X,p),C₀(X,p), c(X,p) and l_∞(X, p) where sequences are taken from a Hausdorff locally convex space X. Besides the investigations of some topological properties we determine topological duals of l(X, p), c₀(X, p) and c(X, p) when considered with the natural linear topologies on them generated by the family of paranorms.