Asplund spaces and a variant of weak uniform rotundity

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...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 2000-06, Vol.61 (3), p.451-454
Main Authors: Giles, John, Vanderwerff, Jon
Format: Article
Language:English
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Summary: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.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700022462