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Weak Compactness and Separation

Published online by Cambridge University Press:  20 November 2018

Robert C. James
Robert C. James*
Affiliation:
Harvey Mudd College and Institute for Advanced Study, Princeton, New Jersey
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The purpose of this paper is to develop characterizations of weakly compact subsets of a Banach space in terms of separation properties. The sets A and B are said to be separated by a hyperplane H if A is contained in one of the two closed half-spaces determined by H, and B is contained in the other; A and B are strictly separated by H if A is contained in one of the two open half-spaces determined by H, and B is contained in the other. The following are known to be true for locally convex topological linear spaces.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 204 - 206
Copyright
Copyright © Canadian Mathematical Society 1964

References

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