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 a locally convex Hausdorff space and we prove some basic facts concerning this spaces.We give complete characterizations for barrelled vector valued spaces and distinguished vector valued Fréchet spaces. At the end we give sufficient conditions guaranteeing that is bornological.