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Weak rotundity in Banach spaces

Published online by Cambridge University Press:  09 April 2009

A. C. Yorke
A. C. Yorke
Affiliation:
Department of Mathematics, University of Newcastle Newcastle, NSW 2308 Australia
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Abstract

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Weak rotundity is defined. One version characterizes the duals of very smooth spaces, another characterizes the duals of extremely smooth spaces. Weak rotundity methods are used to investigate the differentiability of the norm in E**, and to obtain information about quotient spaces, when E** is smooth.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 2 , September 1977 , pp. 224 - 233
Copyright
Copyright © Australian Mathematical Society 1977

References

Cudia, D. F. (1964), “The geometry of Banach spaces. Smoothness”, Trans. Amer. Math. Soc. 110, 284–314.CrossRefGoogle Scholar
Day, M. M. (1973), Normed Linear Spaces, 3rd ed. (Springer-Verlag).CrossRefGoogle Scholar
Giles, J. R. (1971), “On a characterization of differentiability of the norm of a normed linear space”, J. Austral. Math. Soc. 12, 106–114.CrossRefGoogle Scholar
Giles, J. R. (1974), “A non-reflexive Banach space has non-smooth third conjugate space”, Canad. Math. Bull. 17, 117–119.CrossRefGoogle Scholar
Giles, J. R. (1975), “On smoothness of the Banach space embedding”, Bull. Austral. Math. Soc. 13, 69–74.CrossRefGoogle Scholar
Giles, J. R. (1976), “Uniformly weak differentiability of the norm and a condition of Vlasov”, J. Austral. Math. Soc. 21(A), 393–409.CrossRefGoogle Scholar
Klee, V. (1959), “Some new results on smoothness and rotundity in normed linear spaces”, Math. Annalen, 139, 51–63.CrossRefGoogle Scholar
Smith, M. A. (1976), “A smooth non-reflexive second conjugate space”, Bull. Austral. Math. Soc. 15, 29–31.CrossRefGoogle Scholar
Sullivan, F. (1975), “Geometrical properties determined by the higher duals of a Banach space” (preprint).Google Scholar
Zizler, V. (1968), “Banach spaces with differentiable norms”, Comm. Math. Univ. Carol. 8, 3, 415–440.Google Scholar
Zizler, V. (1969), “Some notes on various rotundity and smoothness properties of separable Banach spaces”, Comm. Math. Univ. Carol. 10, 2, 195–206.Google Scholar