Note on strong Aσ-summability

Abstract

The main object of the paper is to study the inclusions [Aσ, p]⊂[Aσ, q], [Aσ, p]⊂[Bσ, q] and [Aσ, p]∩m⊂[Bσ, q] and to characterizae the spaces M([Aσ, p], [Aσ, q]) and M0([Aσ, p]0, [Aσ, q]0). Here [Aσ, p] and [Aσ, q]0 are certain spaces of strongly summable sequences in terms of an injection σ: N→N and anonnegative infinite matrix A, and M([Aσ, p], [Aσ, q]) is the space of summability factors between [Aσ, p] and [Aσ, q].