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Asplund spaces and a variant of weak uniform rotundity

Published online by Cambridge University Press:  17 April 2009

John Giles  and
Jon Vanderwerff
John Giles
Affiliation:
Department of Mathematics, The University of Newcastle, Newcastle NSW 2308, Australia
Jon Vanderwerff
Affiliation:
Department of Mathematics, Le Sierra University, Riverside CA 92515, United States of America
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Abstract

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We introduce a property formally weaker than weak uniform rotundity, which we call equatorial weak uniform rotundity. We show that an equatorially weakly uniformly rotund norm need not be weakly locally uniformly rotund. Nevertheless, we show that an equatorially weakly uniformly rotund Banach space is an Asplund space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 451 - 454
Copyright
Copyright © Australian Mathematical Society 2000

References

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