Valdivia compacta and subspaces of C(K) spaces.
Ondrej F. K. Kalenda (1999)
Extracta Mathematicae
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Displaying similar documents to “Valdivia compact spaces in topology and Banach space theory.”
Valdivia compacta and subspaces of C(K) spaces.
Valdivia compacta and equivalent norms
Ondřej Kalenda (2000)
Studia Mathematica
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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 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’...
A characterization of Valdivia compact spaces.
Ondrej Kalenda (2000)
Collectanea Mathematica
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An Example Concerning Valdivia Compact Spaces
Kalenda, Ondrej (1999)
Serdica Mathematical Journal
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∗ 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...
Complex Banach spaces with Valdivia dual unit ball.
Ondrej F. K. Kalenda (2005)
Extracta Mathematicae
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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.
Simultaneous resolutions of the identity operator in normed spaces.
Manuel Valdivia (1991)
Collectanea Mathematica
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We construct in this paper some simultaneous projective resolutions of the identity operator which we later use to obtain certain new results on quasi-complementation property and Markushevich bases.
Functional-analytic properties of Corson-compact spaces
S. Argyros, S. Mercourakis, S. Negrepontis (1988)
Studia Mathematica
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Complemented and uncomplemented subspaces of Banach spaces.
Anatolij M. Plichko, David Yost (2000)
Extracta Mathematicae
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Does a given Banach space have any non-trivial complemented subspaces? Usually, the answer is: yes, quite a lot. Sometimes the answer is: no, none at all.
Convex sets in Banach spaces and a problem of Rolewicz
A. Granero, M. Jiménez Sevilla, J. Moreno (1998)
Studia Mathematica
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Let be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdorff metric. In the first part of this work we study the density character of and investigate its connections with the geometry of the space, in particular with a property shared by the spaces of Shelah and Kunen. In the second part we are concerned with the problem of Rolewicz, namely the existence of support sets, for the case of spaces C(K).