On the three-space-problem and the lifting of bounded sets
type: Item
instance of: scholarly article
title: On the three-space-problem and the lifting of bounded sets
zbMATH Open document ID: 0803.46001
published in: Collectanea Mathematica
publication date: 1995-01-02T00:00:00Z
full work available at URL: https://eudml.org/doc/41970
review text: The author exhibits a general method to show that for several classes of Fréchet spaces the Three-space-problem fails. This method works for instance for the class of distinguished Fréchet spaces, for Fréchet spaces with the density condition and also for dual Fréchet spaces (which gives a negative answer to a question of D. Vogt). An example of a Banach space, which is not a dual Banach space but the strong dual of a DF-space, shows that there are two really different possibilities of defining the notion of a dual Fréchet space. If in a Three-space-problem the corresponding quotient map is assumed to lift bounded sets, partial positive answers are obtained. Finally, this property of lifting bounded sets gets a special treatment.
Mathematics Subject Classification ID: 46A04
zbMATH DE Number: 633978
zbMATH Keywords: dual Banach-spaces
zbMATH Keywords: three-space-problem
zbMATH Keywords: distinguished Fréchet spaces
zbMATH Keywords: Fréchet spaces with the density condition
zbMATH Keywords: dual Fréchet spaces
zbMATH Keywords: strong dual of a DF-space
zbMATH Keywords: quotient map
zbMATH Keywords: lifting bounded sets
author: Susanne Dierolf
reviewed by: Susanne Dierolf
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 633978