Multiplier convergent series /

Multiplier convergent series /

Saved in:

Bibliographic Details
Author / Creator:	Swartz, Charles, 1938-
Imprint:	Hackensack, N.J. : World Scientific Pub., ©2009.
Description:	1 online resource (x, 253 pages)
Language:	English
Subject:	Convergence. Multipliers (Mathematical analysis) Series, Arithmetic. Orlicz spaces. Convergence. Multipliers (Mathematical analysis) Orlicz spaces. Series, Arithmetic. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11199510

Hidden Bibliographic Details
ISBN:	9789812833884 9812833889 9789812833877 9812833870
Notes:	Includes bibliographical references (pages 245-249) and index. Print version record.
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.
Other form:	Print version: Swartz, Charles, 1938- Multiplier convergent series. Hackensack, N.J. : World Scientific Publishing, ©2009 9789812833877

Description
Summary:	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.
Physical Description:	1 online resource (x, 253 pages)
Bibliography:	Includes bibliographical references (pages 245-249) and index.
ISBN:	9789812833884 9812833889 9789812833877 9812833870