LEADER 03348nam 2200661Ia 450 001 9910456463503321 005 20200520144314.0 010 $a1-282-44092-6 010 $a9786612440922 010 $a981-283-388-9 035 $a(CKB)2550000000001317 035 $a(EBL)477251 035 $a(OCoLC)554919213 035 $a(SSID)ssj0000340647 035 $a(PQKBManifestationID)11265599 035 $a(PQKBTitleCode)TC0000340647 035 $a(PQKBWorkID)10388640 035 $a(PQKB)10999625 035 $a(MiAaPQ)EBC477251 035 $a(WSP)00006977 035 $a(Au-PeEL)EBL477251 035 $a(CaPaEBR)ebr10361610 035 $a(CaONFJC)MIL244092 035 $a(EXLCZ)992550000000001317 100 $a20090306d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMultiplier convergent series$b[electronic resource] /$fCharles Swartz 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$d2009 215 $a1 online resource (264 p.) 300 $aDescription based upon print version of record. 311 $a981-283-387-0 320 $aIncludes bibliographical references (p. 245-249) and index. 327 $aPreface; 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 327 $a14. 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 330 $aIf ? 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 606 $aConvergence 606 $aMultipliers (Mathematical analysis) 606 $aOrlicz spaces 606 $aSeries, Arithmetic 608 $aElectronic books. 615 0$aConvergence. 615 0$aMultipliers (Mathematical analysis) 615 0$aOrlicz spaces. 615 0$aSeries, Arithmetic. 676 $a515.35 676 $a515/.24 700 $aSwartz$b Charles$f1938-$054079 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910456463503321 996 $aMultiplier convergent series$91948799 997 $aUNINA