Displaying similar documents to “An Example Concerning Valdivia Compact Spaces”

Valdivia compacta and equivalent norms

Ondřej Kalenda (2000)

Studia Mathematica

Similarity:

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’...

Complex Banach spaces with Valdivia dual unit ball.

Ondrej F. K. Kalenda (2005)

Extracta Mathematicae

Similarity:

We study the classes of complex Banach spaces with Valdivia dual unit ball. We give complex analogues of several theorems on real spaces. Further we study relationship of these complex Banach spaces with their real versions and that of real Banach spaces and their complexification. We also formulate several open problems.