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 {ek | 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.