Unconditional convergent series on locally convex spaces

摘要

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', β(E', E)) contains no copy of (c_0, ‖·‖_∞) if and only if every continuous linear operator T : E → l_1 is both compact and sequentially compact.