Título: | Spaces of weakly continuous functions. |
Autores: | Ferrera Cuesta, Juan |
Tipo de documento: | texto impreso |
Editorial: | Pacific Journal Mathematics, 1982 |
Dimensiones: | application/pdf |
Nota general: | info:eu-repo/semantics/restrictedAccess |
Idiomas: | |
Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Análisis matemático , Tipo = Artículo |
Resumen: |
This paper is very much in the spirit of a paper by H. Corson [Trans. Amer. Math. Soc. 101 (1961), 1–15; MR0132375 (24 2220)]. Let E be a real Banach space. The bw-topology on E is the finest topology which agrees with the weak topology on all bounded subsets of E. Cwb(E) [Cwbu(E)] is the set of real functions which are weakly continuous [weakly uniformly continuous] on all bounded sets in E. Cwb(E) is always barrelled; a sufficient condition is given for Cwb(E) to be bornological (under the compact-open topology). As a main result, the following are shown to be equivalent: (1) E is reflexive; (ii) Cwbu(E) is a Fr´echet space; (iii) Cwbu(E) is a Pt´ak space; (iv) Cwbu(E) is complete; (v) Cwbu(E) is barrelled; (vi) Cwbu(E) = Cwb(E). |
En línea: | https://eprints.ucm.es/id/eprint/15380/1/18.pdf |
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