UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIES
If λ is a sequence K-space and Σ x j is a series in a topological vector space X; the series is said to be λ-multiplier convergent if the series <img border=0 width=75 height=24 id="_x0000_i1026" src="http:/fbpe/img/proy/v26n1/sumatoria.JPG">conve...
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2007
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| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000100002 |
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oai:scielo:S0716-091720070001000022018-10-30UNIFORM CONVERGENCE OF MULTIPLIER CONVERGENT SERIESSWARTZ,CHARLESIf λ is a sequence K-space and Σ x j is a series in a topological vector space X; the series is said to be λ-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">λ. We show that if λ 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 λ. 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 |
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Scielo Chile |
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Scielo Chile |
| language |
English |
| description |
If λ is a sequence K-space and Σ x j is a series in a topological vector space X; the series is said to be λ-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">λ. We show that if λ 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 λ. A similar uniform convergence result is established for a multiplier convergent series version of the Hahn-Schur Theorem. |
| 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 |
| 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 |
| _version_ |
1718439750521585664 |