Valdivia compact spaces in topology and Banach space theory.
Ondrej F. K. Kalenda (2000)
Extracta Mathematicae
Similarity:
Ondrej F. K. Kalenda (2000)
Extracta Mathematicae
Similarity:
Ondrej Kalenda (2000)
Collectanea Mathematica
Similarity:
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...
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 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’...
Manuel Valdivia (1991)
Collectanea Mathematica
Similarity:
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.
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.
Ofelia Teresa Alas, Mihail G. Tkachenko, Vladimir Vladimirovich Tkachuk, Richard Gordon Wilson, Ivan V. Yashchenko (2001)
Czechoslovak Mathematical Journal
Similarity:
We prove that it is independent of ZFC whether every Hausdorff countable space of weight less than has a dense regular subspace. Examples are given of countable Hausdorff spaces of weight which do not have dense Urysohn subspaces. We also construct an example of a countable Urysohn space, which has no dense completely Hausdorff subspace. On the other hand, we establish that every Hausdorff space of -weight less than has a dense completely Hausdorff (and hence Urysohn) subspace....
S. Argyros, S. Mercourakis, S. Negrepontis (1988)
Studia Mathematica
Similarity: