Uniform boundedness in vector-valued sequence spaces

• 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. 23, Nº. 3, 2004, págs. 235-240
• Idioma: inglés
• DOI: 10.4067/S0716-09172004000300003
• Enlaces
  • Texto completo
• Resumen

  • Let µ be a normal scalar sequence space which is a K-space under the family of semi-norms M and let X be a locally convex space whose topology is generated by the family of semi-norms X. The space µ{X} is the space of all X valued sequences x = {xk} such that {q(xₖ)} ∈ µ{X} for all q ∈ X. The space µ{X} is given the locally convex topology generated by the semi-norms πpq(x) = p({q(xₖ)}), p ∈ X, q ∈ M.We show that if µ satisfies a certain multiplier type of gliding hump property, then pointwise bounded subsets of the β-dual of µ{X} with respect to a locally convex space are uniformly bounded on bounded subsets of µ{X}.

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