Displaying similar documents to “Concrete subspaces and quotient spaces of locally convex spaces and completing sequences”

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.

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...

p-Envelopes of non-locally convex F-spaces

C. M. Eoff (1992)

Annales Polonici Mathematici

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The p-envelope of an F-space is the p-convex analogue of the Fréchet envelope. We show that if an F-space is locally bounded (i.e., a quasi-Banach space) with separating dual, then the p-envelope coincides with the Banach envelope only if the space is already locally convex. By contrast, we give examples of F-spaces with are not locally bounded nor locally convex for which the p-envelope and the Fréchet envelope are the same.