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} ??.\n\nThis 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.Multiplier Convergent Series is written by Swartz Charles W and published by World Scientific. ISBNs for Multiplier Convergent Series are 9789812833884, 9812833889 and the print ISBNs are 9789812833877, 9812833870.