The Banach-Steinhaus Theorem in Abstract Duality Pairs

• Ronglu, Li ^[1] ; Swartz, Charles ^[2]
  1. [1] Harbin Institute of Technology

     Harbin Institute of Technology

     China

     
  2. [2] New Mexico State University

     New Mexico State University

     Estados Unidos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 34, Nº. 4, 2015, págs. 391-399
• Idioma: inglés
• DOI: 10.4067/S0716-09172015000400007
• Enlaces
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• Resumen

  • Let E, F be sets and G a Hausdorff, abelian topological group with b : E X F→ G; we refer to E, F, G as an abstract duality pair with respect to G or an abstract triple and denote this by (E,F : G). Let (Ei,Fi : G) be abstract triples for i = 1, 2. Let Fi be a family of subsets of    Fi    and let    τFi(Ei)    =    τibe    the    topology on    Ei   of uniform convergence on the members of Fi. Let J be a family of mappings from Ei to E2. We consider conditions which guarantee that J is τ1-τ2equicontinuous. We then apply the results to obtain versions of the Banach-Steinhaus Theorem for both abstract triples and for linear operators between locally convex spaces.

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