Gómez Gil, Javier
(1984)
*On local convexity of bounded weak topologies on banach-spaces.*
Pacific Journal of Mathematics, 110
(1).
pp. 71-76.
ISSN 0030-8730

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Official URL: http://projecteuclid.org/euclid.pjm/1102711098

## Abstract

This paper is devoted to the question "Under what conditions on a Banach space E is it true that the bounded weak topology is locally convex?". The theorem of Banach and Dieudonné shows that reflexivity is a sufficient condition. The author proves that reflexivity is also a necessary condition

Item Type: | Article |
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Uncontrolled Keywords: | Duality and reflexivity in normed spaces |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 15819 |

References: | H. S. Collins, Completeness and compactness in linear topological spaces, Trans. Amer. Math. Soc, 79 (1955), 256-280. M. M. Day, Normed Linear Spaces, Berlin 1962. J. Ferrera, Espacios de funciones debilmente continuas sobre espacios de Banach, Tesis Doctoral, Universidad Complutense, Madrid (1980). J. Horvath, Topological Vector Spaces and Distributions, Addison-Wesley, Reading, Massachusetts, 1959. H. P. Rosenthal, Some recent discoveries in the isomorphic theory of Banach Spaces, Bull. H. H. Schaefer, Topological Vector Spaces, Springer-Verlag, Berlin and New York, 1971. R. F. Wheeler, The equicontinuous weak* topology and semi-reflexivity, Studia Mathematica, XLI (1972), 243-256. |

Deposited On: | 03 Jul 2012 11:03 |

Last Modified: | 28 Jan 2016 15:57 |

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