Geodesic
Valdivia compacta and equivalent norms
Studia Mathematica, Tome 138 (2000) no. 2, pp. 179-191

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $ℵ_1$ 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.
DOI : 10.4064/sm-138-2-179-191
Keywords: Corson compact space, Valdivia compact space, projectional resolution of the identity, countably 1-norming Markushevich basis, equivalent norm

Ondřej Kalenda 1

1 
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Ondřej Kalenda. Valdivia compacta and equivalent norms. Studia Mathematica, Tome 138 (2000) no. 2, pp. 179-191. doi: 10.4064/sm-138-2-179-191

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