Multiplier convergent series / Charles Swartz.

Format:

Book

Author/Creator:

Swartz, Charles, 1938-

Language:

English

Subjects (All):

Convergence.

Multipliers (Mathematical analysis).

Orlicz spaces.

Series, Arithmetic.

Physical Description:

1 online resource (264 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, 2009.

Language Note:

English

Summary:

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=18 tjxj converges in X for every {tj} e?. 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 multiplie

Contents:

Preface; Contents; 1. Introduction; 2. Basic Properties of Multiplier Convergent Series; 3. Applications of Multiplier Convergent Series; 4. The Orlicz-Pettis Theorem; 5. Orlicz-Pettis Theorems for the Strong Topology; 6. Orlicz-Pettis Theorems for Linear Operators; 7. The Hahn-Schur Theorem; 8. Spaces of Multiplier Convergent Series and Multipliers; 9. The Antosik Interchange Theorem; 10. Automatic Continuity of Matrix Mappings; 11. Operator Valued Series and Vector Valued Multipliers; 12. Orlicz-Pettis Theorems for Operator Valued Series; 13. Hahn-Schur Theorems for Operator Valued Series

14. Automatic Continuity for Operator Valued MatricesAppendix A. Topological Vector Spaces; Appendix B. Scalar Sequence Spaces; Appendix C. Vector Valued Sequence Spaces; Appendix D. The Antosik-Mikusinski Matrix Theorems; Appendix E. Drewnowski's Lemma; References; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 245-249) and index.

ISBN:

9786612440922

9781282440920

1282440926

9789812833884

9812833889

OCLC:

554919213