Bulletin of the Belgian Mathematical Society - Simon Stevin

On a problem of Horváth concerning barrelled spaces of vector valued continuous functions vanishing at infinity

J.C. Ferrando, J. Kakol, and M. López-Pellicer

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Abstract

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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 11, Number 1 (2004), 127-132.

Dates
First available in Project Euclid: 23 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1080056165

Digital Object Identifier
doi:10.36045/bbms/1080056165

Mathematical Reviews number (MathSciNet)
MR2059181

Zentralblatt MATH identifier
1077.46031

Subjects
Primary: 46A08: Barrelled spaces, bornological spaces 46B25: Classical Banach spaces in the general theory

Keywords
Barrelled space $C_{0}\left(\Omega,X\right)$ spaces

Citation

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 11 (2004), no. 1, 127--132. doi:10.36045/bbms/1080056165. https://projecteuclid.org/euclid.bbms/1080056165


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