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Uniformly weak differentiability of the norm and a condition of Vlasov

Published online by Cambridge University Press:  09 April 2009

J. R. Giles
J. R. Giles
Affiliation:
University of Newcastle, New South Wales, 2308, Australia.
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Abstract

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In determining geometrical conditions on a Banach space under which a Chebychev set is convex, Vlasov (1967) introduced a smoothness condition of some interest in itself. Equivalent forms of this condition are derived and it is related to uniformly weak differentiability of the norm and rotundity of the dual norm.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 4 , June 1976 , pp. 393 - 409
Copyright
Copyright © Australian Mathematical Society 1976

References

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