An inclusion theorem for non-archimedean sequence spaces

Abstract

It is proved that a non-archimedean FK-space E includes the space c₀ of null-sequences if and only if E includes the space l₁` of absolutely summable sequences, and for both inclusions the boundedness in E of the set {e_k | k ∈ N} of the unit vectors is necessary and sufficient.
It is shown that in the non-archimedean context the concepts of wedge space and semiconservative space are equivalent.