On vector-valued sequence spaces

Abstract

In this paper we investigate the topological properties of vector valued sequence spaces. After an introduction of normal Banach sequence spaces λ we consider the vector valued sequence spaces $λ (E),E$ a locally convex Hausdorff space and we prove some basic facts concerning this spaces.We give complete characterizations for barrelled vector valued $DF$ spaces and distinguished vector valued Fréchet spaces. At the end we give sufficient conditions guaranteeing that $λ(E)$ is bornological.