A01=Charles W Swartz
Author_Charles W Swartz
Bounded Multiplier Convergent Series
Category=PBKJ
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Hahn-Schur
HahnAcAEURA"Schur
Hahn–Schur
Multiplier Convergent Series
Orlicz-Pettis
OrliczAcAEURA"Pettis
Orlicz–Pettis
Subseries
Product details
- ISBN 9789812833877
- Publication Date: 11 Dec 2008
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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If λ is a space of scalar-valued sequences, then a series ∑j xj in a topological vector space X is λ-multiplier convergent if the series ∑j=1∞ tjxj converges in X for every {tj} ελ. 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 ι1 are also developed for multiplier convergent series. Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.
