Über analytische Fortsetzung in Banachräumen.
Uncomplementability of spaces of compact operators in larger spaces of operators
In the first part of the paper we prove some new result improving all those already known about the equivalence of the nonexistence of a projection (of any norm) onto the space of compact operators and the containment of in the same space of compact operators. Then we show several results implying that the space of compact operators is uncomplemented by norm one projections in larger spaces of operators. The paper ends with a list of questions naturally rising from old results and the results...
Une caractérisation des simplexes compacts et des cônes réticulés applications
Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms
* Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada).It is shown that the dual unit ball BX∗ of a Banach space X∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a uniformly Gâteaux smooth norm and X is a subspace of a weakly compactly generated space. The bidual unit ball BX∗∗ of a Banach space X∗∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a weakly uniformly rotund norm. In this case...
Uniform Gâteaux smoothness of higher order on separable Banach spaces.
The aim of this paper is to show, among other things, that, in separable Banach spaces, the presence of the smoothness with the highest derivative Lipschitzian implies the uniform Gâteaux smoothness of degree 1 up.
Uniform homeomorphisms between Banach spaces
Uniformly convex norms in spaces with unconditional basis
Uniformly convex operators and martingale type.
The concept of uniform convexity of a Banach space was gen- eralized to linear operators between Banach spaces and studied by Beauzamy [1]. Under this generalization, a Banach space X is uniformly convex if and only if its identity map Ix is. Pisier showe
Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis
*Supported in part by GAˇ CR 201-98-1449 and AV 101 9003. This paper is based on a part of the author’s MSc thesis written under the supervison of Professor V. Zizler.It is shown that a Banach space X admits an equivalent uniformly Gateaux differentiable norm if it has an unconditional basis and X* admits an equivalent norm which is uniformly rotund in every direction.
Universal embeddings of into the space of continuous functions on a product space
Universality, complexity and asymptotically uniformly smooth Banach spaces
For , we show the existence of a Banach space which is both injectively and surjectively universal for the class of all separable Banach spaces with an equivalent -asymptotically uniformly smooth norm. We prove that this class is analytic complete in the class of separable Banach spaces. These results extend previous works by N. J. Kalton, D. Werner and O. Kurka in the case .
Using boundaries to find smooth norms
The aim of this paper is to present a tool used to show that certain Banach spaces can be endowed with smooth equivalent norms. The hypothesis uses particular countable decompositions of certain subsets of , namely boundaries. Of interest is that the main result unifies two quite well known results. In the final section, some new corollaries are given.