Estructuras ordenadas relacionadas con el teorema de la gráfica cerrada

• Autores: Bernardo Cascales Salinas
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 37, Fasc. 1, 1986, págs. 23-53
• Idioma: español
• Títulos paralelos:
  • Ordered structures related to the closed graph theorem
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• Resumen

  • This paper is devoted to the study of some problems and structures concerning with the Closed Graph Theorem. We study the topological vector spaces generated by completing sequences and as a consequence we characterize, in this context, the spaces which are locally complete. We introduce the quasi $L_\Lambda B$-spaces, $\Lambda\subset(0,1]$, and we relate them with the classes of webbed spaces introduced by De Wilde, and the class of spaces with of bounded web studied by the author in a previous paper. For a wide classe of domain spaces, the strictly $\Lambda$-barrelled spaces, we give localization and closed graph theorems when the range spaces the quasi-$L_\Lambda B$-spaces, as well as some lifting properties. When $\Lambda=\{1\}$ our results include that of Valdivia for qualis-$LB$-spaces. A localization result for certain subsets of continuous linear mappings from a strictly $\Lambda$-barrelled space into a quasi-$L_\Lambda B$-space is presented. This result allow us to obtain localization properties for subsets of linear mappings with values in inductive limits that extend previous results by Köthe and De Wilde. New results of localization of bounded subsets in generalized inductive limits are also given.