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  ι1 are also developed for multiplier convergent  series. Finally, the notion of multiplier convergent series is extended to  operator-valued series and vector-valued multipliers.    Contents:  Basic Properties of Multiplier Convergent Series; Applications of  Multiplier Convergent Series; The Orlicz Pettis Theorem; Orlicz-Pettis  Theorems for Strong Topology; Orlicz Pettis Theorems for Linear Operators;  The Hahn Schur Theorem; Spaces of Multiplier Convergent Series and  Multipliers; The Antosik Interchange Theorem; Automatic Continuity of Matrix  Mappings; Operator-Valued Series and Vector-Valued Multipliers;  Orlicz Pettis Theorems for Operator-Valued Series; Hahn Schur Theorems  for Operator-Valued Series; Automatic Continuity for Operator-Valued Matrices.

Multiplier convergent series PDF

The list of books you might like