Valdivia compacta and equivalent norms
Tom 138 / 2000
Studia Mathematica 138 (2000), 179-191
DOI: 10.4064/sm-138-2-179-191
Streszczenie
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.
