On closed subspaces with Schauder bases in non-archimedean Fréchet spaces (Q1866444)

In previous papers, the author surprised the `\(p\)-adic community' by showing that infinite-dimensional Fréchet spaces of countable type over a non-archimedean valued field need not have a Schauder basis. The present paper is a continuation on this successful theme. Among other things, it is shown that (i) a Fréchet space of countable type is normable (nuclear, reflexive, Montal) iff each closed subspace with a Schauder basis has this property, (2) any non-normable Fréchet space contains an infinite-dimensional nuclear closed subspace with a Schauder basis.