Multiplier convergent series /

Multiplier convergent series /

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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

Table of Contents:

Introduction
Basic properties of multiplier convergent series
Applications of multiplier convergent series
The Orlicz-Pettis theorem
Orlicz-Pettis theorems for the strong topology
Orlicz-Pettis theorems for linear operators
The Hahn-Schur theorem
Spaces of multiplier convergent series and multipliers
The Antosik interchange theorem
Automatic continuity of matrix mappings
Operator valued series and vector valued multipliers
Orlicz-Pettis theorems for operator valued series
Hahn-Schur theorems for operator valued series
Automatic continuity for operator valued matrices.