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Valdivia compacta and equivalent norms

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Kalenda O.

Studia Mathematica

2000

tom 138

nr 2

179-191

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.

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1 Studia Mathematica

1 Kalenda O.

1 2000

Wyniki wyszukiwania

Valdivia compacta and equivalent norms