03348nam 2200661Ia 450 991045646350332120200520144314.01-282-44092-69786612440922981-283-388-9(CKB)2550000000001317(EBL)477251(OCoLC)554919213(SSID)ssj0000340647(PQKBManifestationID)11265599(PQKBTitleCode)TC0000340647(PQKBWorkID)10388640(PQKB)10999625(MiAaPQ)EBC477251(WSP)00006977(Au-PeEL)EBL477251(CaPaEBR)ebr10361610(CaONFJC)MIL244092(EXLCZ)99255000000000131720090306d2009 uy 0engur|n|---|||||txtccrMultiplier convergent series[electronic resource] /Charles SwartzSingapore ;Hackensack, NJ World Scientific20091 online resource (264 p.)Description based upon print version of record.981-283-387-0 Includes bibliographical references (p. 245-249) and index.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 Series14. 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; IndexIf ? 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 multiplieConvergenceMultipliers (Mathematical analysis)Orlicz spacesSeries, ArithmeticElectronic books.Convergence.Multipliers (Mathematical analysis)Orlicz spaces.Series, Arithmetic.515.35515/.24Swartz Charles1938-54079MiAaPQMiAaPQMiAaPQBOOK9910456463503321Multiplier convergent series1948799UNINA