Valdivia compacta and equivalent norms
Kalenda, Ondřej
Studia Mathematica, Tome 141 (2000), p. 179-191 / Harvested from The Polish Digital Mathematics Library
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We prove that the dual unit ball of a Banach space X is a Corson compactum provided that the dual unit ball with respect to every equivalent norm on X is a Valdivia compactum. As a corollary we show that the dual unit ball of a Banach space X of density ℵ1 is Corson if (and only if) X has a projectional resolution of the identity with respect to every equivalent norm. These results answer questions asked by M. Fabian, G. Godefroy and V. Zizler and yield a converse to Amir-Lindenstrauss’ theorem.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:216697 
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Kalenda, Ondřej. Valdivia compacta and equivalent norms. Studia Mathematica, Tome 141 (2000) pp. 179-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv138i2p179bwm/

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