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[null,"1.","Record Nr.",null,"UNINA9910456463503321"]
[null,null,"Autore",null,"Swartz Charles <1938->"]
[null,null,"Titolo",null,"Multiplier convergent series [[electronic resource] /] / Charles Swartz"]
[null,null,"Pubbl/distr/stampa",null,"Singapore ; ; Hackensack, NJ, : World Scientific, 2009"]
[null,null,"ISBN",null,"1-282-44092-6"]
[{"$nulls":4},"9786612440922"]
[{"$nulls":4},"981-283-388-9"]
[null,null,"Descrizione fisica",null,"1 online resource (264 p.)"]
[null,null,"Disciplina",null,"515.35"]
[{"$nulls":4},"515/.24"]
[null,null,"Soggetti",null,"Convergence"]
[{"$nulls":4},"Multipliers (Mathematical analysis)"]
[{"$nulls":4},"Orlicz spaces"]
[{"$nulls":4},"Series, Arithmetic"]
[{"$nulls":4},"Electronic books."]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references (p. 245-249) and index."]
[null,null,"Nota di contenuto",null,"Preface; Contents; 1. Introduction; 2. Basic Properties of Multiplier Convergent Series; 3. Applications of Multiplier Convergent Series; 4. The Orlicz-Pettis Theorem; 5. Orlicz-Pettis Theorems for the Strong Topology; 6. Orlicz-Pettis Theorems for Linear Operators; 7. The Hahn-Schur Theorem; 8. Spaces of Multiplier Convergent Series and Multipliers; 9. The Antosik Interchange Theorem; 10. Automatic Continuity of Matrix Mappings; 11. Operator Valued Series and Vector Valued Multipliers; 12. Orlicz-Pettis Theorems for Operator Valued Series; 13. Hahn-Schur Theorems for Operator Valued Series"]
[{"$nulls":4},"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"]
[null,null,null,"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 "]
[{"$nulls":4},"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"]