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A characterisation of weak compactness in Banach spaces

Published online by Cambridge University Press:  17 April 2009

Warren B. Moors
Affiliation:
Department of Mathematics, The University of Auckland, Private Bag 92019Auckland, New Zealand
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In this short note we give a new characterisation of weak compactness.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Bourgain, J. and Talagrand, M., ‘Compacité Extrêmale’, Proc. Amer. Math. Soc. 80 (1980), 6870.CrossRefGoogle Scholar
[2]Khurana, S.S., ‘Pointwise compactness on extreme points’, Proc. Amer. Math. Soc. 83 (1981), 347348.CrossRefGoogle Scholar
[3]Moors, W.B., ‘A selection theorem for weak upper semi-continuous set-valued mappings’, Bull. Austral. Math. Soc. 53 (1996), 213227.CrossRefGoogle Scholar
[4]Namioka, I., ‘A simplification of Khurana's proof’, (unpublished manuscript, 1981).Google Scholar
[5]Rainwater, J., ‘Weak convergence of bounded sequences’, Proc. Amer. Math. Soc. 14 (1963), p. 999.Google Scholar