Non-archimedean topologies of countable type and associated operators

Abstract

Let K be a non-archimedean, non trivially valued, complete field. Given a dual pair of vector spaces (E, F) over K we study the finest locally convex topology of countable type %plane1D;4A5; on E such that (E%plane1D;4A5;′= F and, given a locally convex space E, %plane1D;4A5; we describe the finest topology of countable type on E coarser than %plane1D;4A5; It is also shown how the class (S₀) of spaces of countable type can be obtained from an operator ideal.