Multiplier convergent series [[electronic resource] /] / Charles Swartz
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| Autore: |
Swartz Charles <1938->
|
| Titolo: |
Multiplier convergent series [[electronic resource] /] / Charles Swartz
|
| Pubblicazione: | Singapore ; ; Hackensack, NJ, : World Scientific, 2009 |
| Descrizione fisica: | 1 online resource (264 p.) |
| Disciplina: | 515.35 |
| 515/.24 | |
| Soggetto topico: | Convergence |
| Multipliers (Mathematical analysis) | |
| Orlicz spaces | |
| Series, Arithmetic | |
| Note generali: | Description based upon print version of record. |
| Nota di bibliografia: | Includes bibliographical references (p. 245-249) and index. |
| Nota di contenuto: | 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 | |
| Sommario/riassunto: | 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 |
| Titolo autorizzato: | Multiplier convergent series |
| ISBN: | 1-282-44092-6 |
| 9786612440922 | |
| 981-283-388-9 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910781093603321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |