Let K be a complete,
non-archimedean, non-trivially valued field. Let B be the category of all
non-archimedean Banach spaces over K satisfying the “condition (N)” with
morphisms continuous linear transformations f,|f|≦ 1. In this paper, we first
characterize all compact functors F : B → B as functors which take finite
dimensional spaces to finite dimensional spaces. We then show that in case K is
maximally complete the Mityagin-Shvarts imbedding theorem for duals of functors
holds true for functors in B. Finally, using the above results we show that the dual of
a compact functor is itself compact.
