Note on strong Aσ-summability

Abstract

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