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Structural implications of norms with Hölder right-hand derivatives.

Published online by Cambridge University Press:  17 April 2009

Michael O. Bartlett ,
John R. Giles  and
Jon D. Vanderwerff
Michael O. Bartlett
Affiliation:
Department of MathematicsAvondale College, CooranbongNSW 2265Australia
John R. Giles
Affiliation:
Department of MathematicsThe University of Newcastle, New South Wales 2308Australia
Jon D. Vanderwerff
Affiliation:
Department of MathematicsWalla Walla College, College Place WA 99324United States of America
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Abstract

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We study a nonsmooth extension of Gateaux differentiability satisfying a directional Hölder condition. In particular, we show that a Banach space is an Asplund space if it has an equivalent norm with a directionally Hölder right-hand derivative at each point of its sphere.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 415 - 425
Copyright
Copyright © Australian Mathematical Society 1998

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