Publication: On local convexity of bounded weak topologies on banach-spaces
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1984
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Pacific Journal of Mathematics
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
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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.