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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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1337-2211
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Volume 66, Issue 3

Issues

Multiplier spaces and the summing operator for series

Charles Swartz
Published Online: 2016-08-26 | DOI: https://doi.org/10.1515/ms-2015-0170

Abstract

If {xj} is a sequence in a normed space X, the space of bounded multipliers for the series jxj is defined to be M(xj)={{tj}l:j=1tjxjconverges} and the summing operator S:MxjX is defined to be S({tj})=j=1tjxj. We show that if X is complete, the series jxj is subseries convergent iff the operator S is compact and the series is absolutely convergent iff the operator is absolutely summing. Other related results are established.

MSC 2010: Primary 40A05; 40B05; 40F05; 40J05; 46A45

Key words: multiplier space; summing operator; (weak) compactness; series; convergence; weak sequential continuity; complete continuity

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About the article


Received: 2013-03-01

Accepted: 2013-10-16

Published Online: 2016-08-26

Published in Print: 2016-06-01


Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 687–694, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0170.

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