An abstract Orlics-Pettis theorem and applications

Li Ronglu, Charles Swartz


In this paper we establish two abstract versions of the classical Orlicz-Pettis Theorem for multiplier convergent series. We show that these abstract results yield known versions of the Orlicz-Pettis Theorem for locally convex spaces as well as versions for operator valued series. We also give applications to vector valued measures and spaces of continuous functions.

Palabras clave

Topological vector space; locally convex spaces; convergent series; operators; espacios vectoriales topológicos; espacios localmente convexos; series convergentes; operadores.

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