Uniform convergence of multiplier convergent series

• Swartz, Charles ^[1]
  1. [1] New Mexico State University

     New Mexico State University

     Estados Unidos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 26, Nº. 1, 2007, págs. 27-35
• Idioma: inglés
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• Resumen

  • If λ is a sequence K-space and Pxj is a series in a topological vector space X, the series is said to be λ-multiplier convergent if the series P∞ j=1 tjxj converges in X for every t = {tj} ∈ λ. We show that if λ satisfies a gliding hump condition, called the signed strong gliding hump condition, then the series P∞ j=1 tjxj 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.