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 c...

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Bibliographic Details

Main Author:	Swartz, Charles 1938- (Author)
Format:	Electronic eBook
Language:	English
Published:	Singapore World Scientific Pub. Co. c2009
Subjects:	Convergence Series, Arithmetic Multipliers (Mathematical analysis) Orlicz spaces
Online Access:	FHN01 Volltext
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
Physical Description:	x, 253 p
ISBN:	9789812833884