UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES

UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES

If &#955; is a sequence K-space and &#931; x j is a series in a topological vector space X; the series is said to be &#955;-multiplier convergent if the series <img border=0 width=75 height=24 id="_x0000_i1026" src="http:/fbpe/img/proy/v26n1/sumatoria.JPG">converges in X for every t = {tj} <img border=0 width=15 height=15 id="_x0000_i1027" src="http:/fbpe/img/proy/v26n1/pertenece.JPG">&#955;. We show that if &#955; satisfies a gliding hump condition, called the signed strong gliding hump condition, then the series <img border=0 width=75 height=24 id="_x0000_i1028" src="http:/fbpe/img/proy/v26n1/sumatoria.JPG">converge uniformly for t = {tj} belonging to bounded subsets of &#955;. A similar uniform convergence result is established for a multiplier convergent series version of the Hahn-Schur Theorem.

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Main Author: SWARTZ,CHARLES
Format: Digital revista
Language:English
Published: Universidad Católica del Norte, Departamento de Matemáticas 2007
Online Access:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000100002
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spelling oai:scielo:S0716-091720070001000022018-10-30UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIESSWARTZ,CHARLESIf &#955; is a sequence K-space and &#931; x j is a series in a topological vector space X; the series is said to be &#955;-multiplier convergent if the series <img border=0 width=75 height=24 id="_x0000_i1026" src="http:/fbpe/img/proy/v26n1/sumatoria.JPG">converges in X for every t = {tj} <img border=0 width=15 height=15 id="_x0000_i1027" src="http:/fbpe/img/proy/v26n1/pertenece.JPG">&#955;. We show that if &#955; satisfies a gliding hump condition, called the signed strong gliding hump condition, then the series <img border=0 width=75 height=24 id="_x0000_i1028" src="http:/fbpe/img/proy/v26n1/sumatoria.JPG">converge uniformly for t = {tj} belonging to bounded subsets of &#955;. A similar uniform convergence result is established for a multiplier convergent series version of the Hahn-Schur Theorem.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.26 n.1 20072007-05-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000100002en10.4067/S0716-09172007000100002
institution SCIELO
collection OJS
country Chile
countrycode CL
component Revista
access En linea
databasecode rev-scielo-cl
tag revista
region America del Sur
libraryname SciELO
language English
format Digital
author SWARTZ,CHARLES
spellingShingle SWARTZ,CHARLES
UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES
author_facet SWARTZ,CHARLES
author_sort SWARTZ,CHARLES
title UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES
title_short UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES
title_full UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES
title_fullStr UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES
title_full_unstemmed UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES
title_sort uniform convergence of multiplier convergent series
description If &#955; is a sequence K-space and &#931; x j is a series in a topological vector space X; the series is said to be &#955;-multiplier convergent if the series <img border=0 width=75 height=24 id="_x0000_i1026" src="http:/fbpe/img/proy/v26n1/sumatoria.JPG">converges in X for every t = {tj} <img border=0 width=15 height=15 id="_x0000_i1027" src="http:/fbpe/img/proy/v26n1/pertenece.JPG">&#955;. We show that if &#955; satisfies a gliding hump condition, called the signed strong gliding hump condition, then the series <img border=0 width=75 height=24 id="_x0000_i1028" src="http:/fbpe/img/proy/v26n1/sumatoria.JPG">converge uniformly for t = {tj} belonging to bounded subsets of &#955;. A similar uniform convergence result is established for a multiplier convergent series version of the Hahn-Schur Theorem.
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2007
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000100002
work_keys_str_mv AT swartzcharles uniformconvergenceofmultiplierconvergentseries
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