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On the drop and weak drop properties for a Banach space

Published online by Cambridge University Press:  17 April 2009

J.R. Giles ,
Brailey Sims  and
A.C. Yorke
J.R. Giles
Affiliation:
Department of Mathematics, The University of Newcastle, Newcastle NSW 2308, Australia
Brailey Sims
Affiliation:
Department of Mathematics, The University of Newcastle, Newcastle NSW 2308, Australia
A.C. Yorke
Affiliation:
Department of Mathematics, The University of Newcastle, Newcastle NSW 2308, Australia
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Rolewicz' drop property is a modification of a concept underlying Daneš' drop theorem. We characterise the drop property by the upper semicontinuity and compact valued property of the duality mapping for the dual. The characterisation suggests that we define a weak drop property which we show characterises the reflexivity of the space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 3 , June 1990 , pp. 503 - 507
Copyright
Copyright © Australian Mathematical Society 1990

References

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