On a problem of Horváth concerning barrelled spaces of vector valued continuous functions vanishing at infinity
Ferrando, J.C. ; Kakol, J. ; López-Pellicer, M.
Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, p. 127-132 / Harvested from Project Euclid
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Let $C_{0}\left( \Omega ,X\right)$ be the linear space of all continuous functions from a locally compact normal space $\Omega $ into a normed space $X$ vanishing at infinity, equipped with the supremum-norm topology. The main result of the paper says that if $X$ is barrelled, then the space $C_{0}\left( \Omega ,X\right) $ is always barrelled. This answers a question posed by J. Horváth.
Publié le : 2004-03-14
Classification:  Barrelled space,  $C_{0}\left(\Omega,X\right)$ spaces,  46A08,  46B25 
@article{1080056165,
     author = {Ferrando, J.C. and Kakol, J. and L\'opez-Pellicer, M.},
     title = {On a problem of Horv\'ath concerning
barrelled spaces of vector valued
continuous functions vanishing at infinity},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {11},
     number = {1},
     year = {2004},
     pages = { 127-132},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1080056165}
}

Ferrando, J.C.; Kakol, J.; López-Pellicer, M. On a problem of Horváth concerning
barrelled spaces of vector valued
continuous functions vanishing at infinity. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, pp.  127-132. http://gdmltest.u-ga.fr/item/1080056165/