Banach-Mackey, locally complete spaces, and ℓ_p,q-summability

Abstract

We defined the ℓ_p,q-summability property and study the relations between the ℓ_p,q-summability property, the Banach-Mackey spaces and the locally complete spaces.We prove that, for c₀-quasibarrelled spaces, Banach-Mackey and locally complete are equivalent. Last section is devoted to the study of CS-closed sets introduced by Jameson and Kakol.