Reflexivity and AK-property of certain vector sequence spaces

Abstract

Let $E$ be a Banach space and $\Lambda$ a Banach perfect sequence space. Denote by $\Lambda (E)$ the space of all $\Lambda$-summable sequences from $E$. In this note it is proved that $\Lambda (E)$ is reflexive if and only if $\Lambda$ and $E$ are reflexive and each member of $\Lambda (E)$ is the limit of its finite sections.