Multiplier Convergent Series

Multiplier Convergent Series

By: Charles Swartz (author)Hardback

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Description

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.

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.

Product Details

  • ISBN13: 9789812833877
  • Format: Hardback
  • Number Of Pages: 264
  • ID: 9789812833877
  • ISBN10: 9812833870

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