Displaying similar documents to “Gâteaux smooth partitions of unity on weakly compactly generated Banach spaces”

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...

Some properties on the closed subsets in Banach spaces

Abdelhakim Maaden, Abdelkader Stouti (2006)

Archivum Mathematicum

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It is shown that under natural assumptions, there exists a linear functional does not have supremum on a closed bounded subset. That is the James Theorem for non-convex bodies. Also, a non-linear version of the Bishop-Phelps Theorem and a geometrical version of the formula of the subdifferential of the sum of two functions are obtained.

Functions locally dependent on finitely many coordinates.

Petr Hájek, Václav Zizler (2006)

RACSAM

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The notion of functions dependent locally on finitely many coordinates plays an important role in the theory of smoothness and renormings on Banach spaces, especially when higher smoothness (C) is involved. In this note we survey most of the main results in this area, and indicate many old as well as new open problems.