2026-06-01T02:36:21Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/646242023-08-25T10:28:40Zcom_20.500.14352_14col_20.500.14352_15

Spaces of weakly continuous functions. Ferrera Cuesta, Juan 517.986.6 517.518.45 Análisis matemático 1202 Análisis y Análisis Funcional 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). Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-21T02:01:40Z 2023-06-21T02:01:40Z 1982 journal article https://hdl.handle.net/20.500.14352/64624 0030-8730 eng restricted access application/pdf Pacific Journal Mathematics