Multiplier convergent series
Book information
Description
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.
Similar books
Abstract Duality Pairs in Analysis
2018 · PDF
Measure, Integration And Function Spaces
1994 · DJVU
Elementary Functional Analysis
2009 · DJVU
Multiplier Convergent Series
2008 · PDF
Introduction to Real Analysis
1998 · PDF
Introduction to Real Analysis
1988 · DJVU
Measure, Integration And Function Spaces
1994 · DJVU
Elementary Functional Analysis
2009 · DJVU