Vol. 39, No. 3, 1971

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Compact functors in categories of non-archimedean Banach spaces

Kung-Wei Yang

Vol. 39 (1971), No. 3, 821–826

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.

Mathematical Subject Classification 2000
Primary: 46M15
Received: 19 August 1970
Published: 1 December 1971
Kung-Wei Yang