Displaying similar documents to “On the structure of G-spaces”

Concrete subspaces and quotient spaces of locally convex spaces and completing sequences

Süleyman Önal, Tosun Terzioğlu

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CONTENTSIntroduction..................................................................................51. Almost bounded sets and operators........................................62. Eidelheit’s theorem................................................................133. Nuclear Köthe quotients.........................................................204. Nuclear Köthe subspaces and completing sequences...........225. Applications...........................................................................256....

Enlargements of operators between locally convex spaces.

José A. Conejero (2007)

RACSAM

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In this note we study three operators which are canonically associated with a given linear and continuous operator between locally convex spaces. These operators are defined using the spaces of bounded sequences and null sequences. We investigate the relation between them and the original operator concerning properties, like being surjective or a homomorphism.

Strong proximinality and polyhedral spaces.

Gilles Godefroy, V. Indumathi (2001)

Revista Matemática Complutense

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In any dual space X*, the set QP of quasi-polyhedral points is contained in the set SSD of points of strong subdifferentiability of the norm which is itself contained in the set NA of norm attaining functionals. We show that NA and SSD coincide if and only if every proximinal hyperplane of X is strongly proximinal, and that if QP and NA coincide then every finite codimensional proximinal subspace of X is strongly proximinal. Natural examples and applications are provided.

Fréchet directional differentiability and Fréchet differentiability

John R. Giles, Scott Sciffer (1996)

Commentationes Mathematicae Universitatis Carolinae

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Zaj’ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any real-valued function on a normed linear space, the set of points where the function is Fréchet directionally differentiable but not Fréchet differentiable...