Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(5): 1579-1586

Printed September 30, 2015

https://doi.org/10.4134/BKMS.2015.52.5.1579

Copyright © The Korean Mathematical Society.

Barrelledness of some spaces of vector measures and bounded linear operators

Juan Carlos Ferrando

Universidad Miguel Hern\'{a}ndez

Abstract

In this paper we investigate the barrellednes of some spaces of $X$-valued measures, $X$ being a barrelled normed space, and provide examples of non barrelled spaces of bounded linear operators from a Banach space $X$ into a barrelled normed space $Y$, equipped with the uniform convergence topology.

Keywords: barrelled space, vector measure, bounded linear operator, projective and injective tensor product, Radon-Nikod\'{y}m property

MSC numbers: 46A08, 46G10, 46B28

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