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On local convexity of bounded weak topologies on banach-spaces

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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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
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:06 Feb 2014 10:32

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