(1) Departamento de Matemáticas, Universidad de Cádiz, Apdo, 40, 11510-Puerto Real (Cádiz), Spain
Abstract:
In this paper we will study some families and subalgebras ℱ of ℙ (ℕ) that let us characterize the unconditional convergence of series through the weak convergence of subseries ℱ. As a consequence, we obtain a new version of the Orlicz–Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.
ℱ. As a consequence, we obtain a new version of the Orlicz–Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.