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Multiplier Convergent Series, Hardback Book

Multiplier Convergent Series Hardback

Hardback

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If 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=1 tjxj converges in X for every {tj} .

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 multiplier convergent series.

Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.

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