Consequences of the existence of a non-compact operator between nuclear Köthe spaces
type: Item
instance of: scholarly article
title: Consequences of the existence of a non-compact operator between nuclear Köthe spaces
zbMATH Open document ID: 0545.46006
DOI: 10.1007/BF01174583
author: Zafer Nurlu
author: A. Tosun Terz{i}oğlu
published in: Manuscripta Mathematica
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155001
review text: Let E and F be nuclear Köthe spaces with continuous norm. Then using the result: ''Every linear continuous map form E into F is compact if and only if every continuous generalized diagonal map (i.e. composition of a permutation by a diagonal map) from E into F is compact'', it is proved that if there exists a non-compact linear continuous map from E into F then E and F have a common step space up to isomorphism in each of the following cases: 1) E is regular and F is isomorphic to a subspace of E. 2) F is regular and E is isomorphic to a quotient space of F. 3) E and F satisfy a certain splitting condition. Consequences in some particular cases are also obtained.
Mathematics Subject Classification ID: 46A45
Mathematics Subject Classification ID: 46A13
Mathematics Subject Classification ID: 46A11
Mathematics Subject Classification ID: 47B37
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 3867988
zbMATH Keywords: existence of a non-compact operator
zbMATH Keywords: nuclear Köthe spaces with continuous norm
zbMATH Keywords: continuous generalized diagonal map
zbMATH Keywords: subspace
zbMATH Keywords: quotient space
zbMATH Keywords: splitting condition
MaRDI profile type: Publication
cites work: Q3310365
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OpenAlex ID: W2068402234
description: scientific article; zbMATH DE number 3867988