Orlicz-Pettis Theorems for Multiplier Convergent Series

Abstract

Orlicz-Pettis theorems have been established for multiplier convergent series where the multipliers come from $c_0$ or $l^p(0<p<\infty )$. We show that these results as well as the classical Orlicz-Pettis theorem are corollaries of a general result based on the fact that all of these multiplier spaces have the canonical unit vectors as a Schauder basis.