Multiplier Convergent Series

If is a space of scalar-valued sequences, then a series j xj in a topological vector space X is -multiplier convergent if the series j=1 tjxj converges in X for every {tj} . This monograph studies properties of such series and gives applications to topics in locally convex spaces and vector-valued measures. A number of versions of the Orlicz-Pettis theorem are derived for multiplier convergent series with respect to various locally convex topologies. Variants of the classical Hahn-Schur theorem on the equivalence of weak and norm convergent series in 1 are also developed for multiplier convergent series. Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.