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Weak compactness in locally convex spaces

Published online by Cambridge University Press:  18 May 2009

I. Tweddle
I. Tweddle
Affiliation:
University of GlasgowGlasgow, W.2.
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In [2], R. C. James proved that a weakly closed subset X of a real Banach space is weakly compact if and only if each continuous linear form attains its supremum on X. He also extended the result to the locally convex case, and, in [5], J. D. Pryce gave a simplified proof of the general result that is recorded below for reference in the sequel.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 9 , Issue 2 , July 1968 , pp. 123 - 127
Copyright
Copyright © Glasgow Mathematical Journal Trust 1968

References

REFERENCES

1.Bartle, R. G., Dunford, N. and Schwartz, J., Weak compactness and vector measures, Can. J. Math. 7 (1955), 289–305.CrossRefGoogle Scholar
2.James, R. C., Weakly compact sets, Trans. Amer. Math. Soc. 113 (1964), 129–140.CrossRefGoogle Scholar
3.Kelley, J. L., Namioka, I. et al. , Linear Topological Spaces (Princeton, 1963).CrossRefGoogle Scholar
4.Köthe, G., Topologische Lineare Räume I (Berlin, Göttingen, Heidelberg, 1960).CrossRefGoogle Scholar
5.Pryce, J. D., Weak compactness in locally convex spaces, Proc. Amer. Math. Soc. 17 (1) (1966), 148–155.CrossRefGoogle Scholar
6.Rainwater, J., Weak convergence of bounded sequences, Proc. Amer. Math. Soc. 14 (1963), 999.Google Scholar
7.Robertson, A. P. and Robertson, W. J., Topological Vector Spaces (Cambridge, 1963).Google Scholar
8.Saks, S., Theory of the Integral, 2nd revised edition (New York).Google Scholar