Hidden Bibliographic Details
| ISBN: | 9789812833884
9812833889
9789812833877
9812833870
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| Notes: | Includes bibliographical references (pages 245-249) and index.
Print version record.
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| Summary: | If [symbol] is a space of scalar-valued sequences, then a series [symbol] xj in a topological vector space X is [symbol]-multiplier convergent if the series [symbol] tjxj converges in X for every [symbol]. 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 [symbol] are also developed for multiplier convergent series. Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.
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| Other form: | Print version: Swartz, Charles, 1938- Multiplier convergent series. Hackensack, N.J. : World Scientific Publishing, ©2009 9789812833877
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