On quotients of Köthe sequence spaces of infinite order
type: Item
instance of: scholarly article
title: On quotients of Köthe sequence spaces of infinite order
zbMATH Open document ID: 0858.46010
DOI: 10.1007/BF01195706
published in: Archiv der Mathematik
publication date: 1997-03-25T00:00:00Z
review text: For a Köthe sequence space \(E=\lambda_\infty(A)\) the authors prove that the following conditions are equivalent: (a) \(E\) is quasinormable. (b) Every quotient of \(E\) satisfies the density condition. (c) Every separable quotient of \(E\) is reflexive. (d) \(E\) satisfies the local Grothendieck property. It is also proved here that \(E\) always satisfies the Grothendieck property (i.e. every \(\sigma(E',E)\)-null sequence is \(\sigma(E',E'')\)-null).
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A04
Mathematics Subject Classification ID: 46A11
zbMATH DE Number: 938527
zbMATH Keywords: Köthe sequence space
zbMATH Keywords: quasinormable
zbMATH Keywords: density condition
zbMATH Keywords: separable quotient
zbMATH Keywords: reflexive
zbMATH Keywords: local Grothendieck property
author: Juan Carlos Díaz
author: Carmen Fernández
MaRDI profile type: Publication
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cites work: Stefan Heinrich's Density Condition for Fréchet Spaces and the Characterization of the Distinguished Köthe Echelon Spaces
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cites work: Q3971371
cites work: Q5183990
cites work: Unbounded linear operators and nuclear Köthe quotients
cites work: Q3951046
cites work: A characterization of totally reflexive Fréchet spaces
full work available at URL: https://doi.org/10.1007/bf01195706
OpenAlex ID: W2047799184
description: scientific article; zbMATH DE number 938527