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AN ELEMENTARY PROOF OF JAMES’ CHARACTERISATION OF WEAK COMPACTNESS. II

Published online by Cambridge University Press:  26 September 2016

WARREN B. MOORS*
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019 Auckland, New Zealand email [email protected]
SAMUEL J. WHITE
Affiliation:
Department of Mathematics, University of Auckland, Private Bag 92019 Auckland, New Zealand email [email protected]
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Abstract

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In this paper we provide an elementary proof of James’ characterisation of weak compactness for Banach spaces whose dual ball is weak sequentially compact.

Type
Research Article
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

Deville, R., Godefroy, G. and Zizler, V., Smoothness and Renormings in Banach Spaces, Pitman Monographs and Surveys in Pure and Applied Mathematics, 64 (Longman Scientific and Technical, Harlow, 1993), (copublished in the United States with John Wiley, New York).Google Scholar
Hagler, J. and Sullivan, F., ‘Smoothness and weak* sequential compactness’, Proc. Amer. Math. Soc. 78 (1980), 497503.Google Scholar
James, R. C., ‘Weakly compact sets’, Trans. Amer. Math. Soc. 113 (1964), 129140.Google Scholar
Larman, D. and Phelps, R. R., ‘Gateaux differentiability of convex functions on Banach spaces’, J. Lond. Math. Soc. (2) 20 (1979), 115127.Google Scholar
Moors, W. B., ‘An elementary proof of James’ characterisation of weak compactness’, Bull. Aust. Math. Soc. 84 (2011), 98102.Google Scholar
Pryce, J. D., ‘Weak compactness in locally convex spaces’, Proc. Amer. Math. Soc. 17 (1966), 148155.Google Scholar