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A finite dimensional reduction of the Schauder Conjecture

Espedito De Pascale (1993)

Commentationes Mathematicae Universitatis Carolinae

Schauder’s Conjecture (i.eėvery compact convex set in a Hausdorff topological vector space has the f.p.p.) is reduced to the search for fixed points of suitable multivalued maps in finite dimensional spaces.

A Lifting Result for Locally Pseudo-Convex Subspaces of L₀

Félix Cabello Sánchez (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

It is shown that if F is a topological vector space containing a complete, locally pseudo-convex subspace E such that F/E = L₀ then E is complemented in F and so F = E⊕ L₀. This generalizes results by Kalton and Peck and Faber.

A note on a theorem of Klee

Jerzy Kąkol (1993)

Commentationes Mathematicae Universitatis Carolinae

It is proved that if E , F are separable quasi-Banach spaces, then E × F contains a dense dual-separating subspace if either E or F has this property.

A rigid space admitting compact operators

Paul Sisson (1995)

Studia Mathematica

A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. The first complete rigid space was published in 1981 in [2]. Clearly a rigid space is a trivial-dual space, and admits no compact endomorphisms. In this paper a modification of the original construction results in a rigid space which is, however, the domain space of a compact operator, answering a question that was first raised soon after the existence of complete rigid spaces was...

A uniform boundedness principle of Pták

Charles W. Swartz (1993)

Commentationes Mathematicae Universitatis Carolinae

The Antosik-Mikusinski Matrix Theorem is used to give an extension of a uniform boundedness principle due to V. Pták to certain metric linear spaces. An application to bilinear operators is given.

Banach spaces, à la recherche du temps perdu.

Jesús M. Fernández Castillo (2000)

Extracta Mathematicae

What follows is the opening conference of the late night seminar at the III Conference on Banach Spaces held at Jarandilla de la Vera, Cáceres. Maybe the reader should not take everything what follows too seriously: after all, it was designed for a friendly seminar, late in the night, talking about things around a table shared by whisky, preprints and almonds. Maybe the reader should not completely discard it. Be as it may, it seems to me by now that everything arrives in the nick of time. A twisted...

Bayoumi Quasi-Differential is different from Fréchet-Differential

Aboubakr Bayoumi (2006)

Open Mathematics

We prove that the Quasi Differential of Bayoumi of maps between locally bounded F-spaces may not be Fréchet-Differential and vice versa. So a new concept has been discovered with rich applications (see [1–6]). Our F-spaces here are not necessarily locally convex

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