UNCONDITIONAL CONVERGENT SERIES ON LOCALLY CONVEX SPACES

Abstract

A characterization of unconditional convergent series is given for the case of sequentially complete locally convex spaces. From it we show that if $E$ is a barrelled space with continuous dual $E'$, then ($E'$, $\beta (E'$, $E$)) contains no copy of ($c_0,~\|\cdot \|_\infty$) if and only if every continuous linear operator $T:E\to l_1$ is both compact and sequentially compact.