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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| Autor principal: | |
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| Lenguaje: | English |
| Publicado: |
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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| Sumario: | 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. |
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