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Displaying similar documents to “Simultaneous resolutions of the identity operator in normed spaces.”

An Example Concerning Valdivia Compact Spaces

Kalenda, Ondrej (1999)

Serdica Mathematical Journal

Similarity:

∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998 We prove that the dual unit ball of the space C0 [0, ω1 ) endowed with the weak* topology is not a Valdivia compact. This answers a question posed to the author by V. Zizler and has several consequences. Namely, it yields an example of an affine continuous image of a convex Valdivia compact (in the weak* topology of a dual Banach space) which is not Valdivia, and shows that the property of the dual unit ball being...

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.