Abstract:In this paper, we show the representation of K\"othe dual of Banach sequence spaces $\ell _p[X]$ $(1\leq p< \infty )$ and give a characterization of that the spaces $\ell _p[X]$ $(1< p< \infty )$ are Grothendieck spaces.
Keywords: vector-valued sequence space; K\"othe dual; GAK-space; Grothendieck space
AMS Subject Classification: 46B16