Gâteaux smooth partitions of unity on weakly compactly generated Banach spaces
K. John, V. Zizler (1977)
Studia Mathematica
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Displaying similar documents to “Uniformly smooth partitions of unity on superreflexive Banach spaces”
Gâteaux smooth partitions of unity on weakly compactly generated Banach spaces
Smooth partitions of unity on some non-separable Banach spaces
H. Toruńczyk (1973)
Studia Mathematica
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Smoothness in Banach spaces. Selected problems.
Marian Fabian, Vicente Montesinos, Václav Zizler (2006)
RACSAM
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This is a short survey on some recent as well as classical results and open problems in smoothness and renormings of Banach spaces. Applications in general topology and nonlinear analysis are considered. A few new results and new proofs are included. An effort has been made that a young researcher may enjoy going through it without any special pre-requisites and get a feeling about this area of Banach space theory. Many open problems of different level of difficulty are discussed. For...
On non-midpoint locally uniformly rotund normability in Banach spaces.
Mirmostafaee, A.K. (2004)
International Journal of Mathematics and Mathematical Sciences
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On WCG Banach spaces with norms which are uniformly differentiable in every direction
Kutzarova, D. N., Troyanski, S. L.
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Uniformly Gâteaux Differentiable Norms in Spaces with Unconditional Basis
Rychter, Jan (2000)
Serdica Mathematical Journal
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*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.
On two classes of Banach spaces with uniform normal structure
Ji Gao, Ka-Sing Lau (1991)
Studia Mathematica
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Rolle's theorem and negligibility of points in infinite dimensional Banach spaces.
D. Azagra, J. Gómez, J. A. Jaramillo (1996)
Extracta Mathematicae
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Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms
Fabian, Marián, Hájek, Petr, Zizler, Václav (1997)
Serdica Mathematical Journal
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* 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...