Multiplier Convergent Series by Charles W Swartz (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review This thoughtful book, carefully written by a renowned specialist in convergence of series in topological vector spaces, will soon be a standard reference and source of further research in the area. –Mathematical ReviewsThis is a well-written book on the state of the art of multiplier convergent series and their applications … The author has highly succeeded in presenting this exciting subject. –Zentralblatt MATH

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