The density condition in quotients of quasinormable Fréchet spaces. II
type: Item
instance of: scholarly article
title: The density condition in quotients of quasinormable Fréchet spaces. II
zbMATH Open document ID: 0949.46001
author: Angela A. Albanese
published in: Revista Matemática Complutense
publication date: 2000-08-27T00:00:00Z
full work available at URL: https://eudml.org/doc/44426
review text: With this paper, the author answers positively an open problem about the Heinrich density condition in quotients of Fréchet spaces. The problem was solved partially by the same author in part I [Stud. Math. 125, No. 2, 131-141 (1997; Zbl 0912.46001)], where she showed that a separable Fréchet space is quasinormable if, and only if, every quotient space satisfies the Heinrich density condition. Here the same statement is proved without the hypothesis of separability. The problem was proposed by \textit{J. Bonet} and \textit{J. C. Diaz}. They proved [Monatsh. Math. 117, No. 3-4, 199-212 (1994; Zbl 0804.46002)] that every Köthe echelon space of order \(p\) \((1< p<\infty)\) which is not quasinormable, has a separated quotient which does not satisfy the Heinrich density condition.
Mathematics Subject Classification ID: 46A04
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A11
zbMATH DE Number: 1330679
zbMATH Keywords: quasinormable Fréchet spaces
zbMATH Keywords: Heinrich density condition
zbMATH Keywords: Köthe echelon space
reviewed by: M. J. Chasco
MaRDI profile type: Publication
OpenAlex ID: W2122035900
DOI: 10.5209/REV_REMA.1999.V12.N1.17191
description: scientific article; zbMATH DE number 1330679