Dense subspaces of quasinormable spaces
Identifieur interne : 000E41 ( Istex/Corpus ); précédent : 000E40; suivant : 000E42Dense subspaces of quasinormable spaces
Auteurs : José Bonet ; Susanne Dierolf ; Khin Aye AyeSource :
- Mathematische Nachrichten [ 0025-584X ] ; 2006-05.
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Abstract
Dense linear subspaces of quasinormable Fréchet spaces need not be quasinormable, as an example due to J. Bonet and S. Dierolf proved. A characterization of the quasinormability of dense linear subspaces of quasinormable locally convex spaces and several consequences are given. Moreover, an example of a dense linear subspace of a countable direct sum of Banach spaces, which is not quasinormable, is provided. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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DOI: 10.1002/mana.200310386
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Vogt</name></json:item></author><host><volume>85</volume><pages><last>197</last><first>163</first></pages><author></author><title>Studia Math.</title></host><title>On the functor Ext (E, F ) for Fréchet spaces</title></json:item></refBibs><genre><json:string>article</json:string></genre><host><volume>279</volume><publisherId><json:string>MANA</json:string></publisherId><pages><total>6</total><last>704</last><first>699</first></pages><issn><json:string>0025-584X</json:string></issn><issue>7</issue><subject><json:item><value>Original Paper</value></json:item></subject><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1522-2616</json:string></eissn><title>Mathematische Nachrichten</title><doi><json:string>10.1002/(ISSN)1522-2616</json:string></doi></host><categories><wos><json:string>science</json:string><json:string>mathematics</json:string></wos><scienceMetrix><json:string>natural sciences</json:string><json:string>mathematics & statistics</json:string><json:string>general mathematics</json:string></scienceMetrix></categories><publicationDate>2006</publicationDate><copyrightDate>2006</copyrightDate><doi><json:string>10.1002/mana.200310386</json:string></doi><id>D1C051F864B94C046641727F04A19E45162E0EDF</id><score>0.3681961</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/D1C051F864B94C046641727F04A19E45162E0EDF/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/D1C051F864B94C046641727F04A19E45162E0EDF/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/D1C051F864B94C046641727F04A19E45162E0EDF/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Dense subspaces of quasinormable spaces</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>WILEY‐VCH Verlag</publisher><pubPlace>Berlin</pubPlace><availability><p>Copyright © 2006 WILEY‐VCH Verlag GmbH & Co. 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KGaA, Weinheim)</p></abstract></abstractGroup></contentMeta><noteGroup><note xml:id="fn1"><p>Phone: +49 651 201 3511, Fax: +49 651 201 3935</p></note></noteGroup></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Dense subspaces of quasinormable spaces</title></titleInfo><titleInfo type="abbreviated" lang="en"><title>Dense subspaces of quasinormable spaces</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Dense subspaces of quasinormable spaces</title></titleInfo><name type="personal"><namePart type="given">José</namePart><namePart type="family">Bonet</namePart><affiliation>ETS Arquitectura, Departamento De Matemática Aplicada, Universidad Politécnica de Valencia, E‐46071 Valencia, Spain</affiliation><affiliation>Phone: +34 963 877 662, Fax: +34 963 877 669</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Susanne</namePart><namePart type="family">Dierolf</namePart><affiliation>Fachbereich IV – Mathematik, Universität Trier, 54286 Trier, Germany</affiliation><description>Phone: +49 651 201 3511, Fax: +49 651 201 3935</description><affiliation>E-mail: sdierolf@uni‐trier.de</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Khin</namePart><namePart type="family">Aye Aye</namePart><affiliation>Department of Mathematics, University of Yangon, Yangon (Myanmar)</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="article" displayLabel="article"></genre><originInfo><publisher>WILEY‐VCH Verlag</publisher><place><placeTerm type="text">Berlin</placeTerm></place><dateIssued encoding="w3cdtf">2006-05</dateIssued><dateCaptured encoding="w3cdtf">2003-11-03</dateCaptured><dateValid encoding="w3cdtf">2004-09-21</dateValid><copyrightDate encoding="w3cdtf">2006</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><extent unit="references">20</extent></physicalDescription><abstract lang="en">Dense linear subspaces of quasinormable Fréchet spaces need not be quasinormable, as an example due to J. Bonet and S. Dierolf proved. A characterization of the quasinormability of dense linear subspaces of quasinormable locally convex spaces and several consequences are given. Moreover, an example of a dense linear subspace of a countable direct sum of Banach spaces, which is not quasinormable, is provided. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)</abstract><subject lang="en"><genre>keywords</genre><topic>Fréchet spaces</topic><topic>(DF)‐spaces</topic><topic>quasinormable spaces</topic><topic>locally convex spaces</topic></subject><relatedItem type="host"><titleInfo><title>Mathematische Nachrichten</title></titleInfo><titleInfo type="abbreviated"><title>Math. Nachr.</title></titleInfo><genre type="journal">journal</genre><subject><genre>article-category</genre><topic>Original Paper</topic></subject><identifier type="ISSN">0025-584X</identifier><identifier type="eISSN">1522-2616</identifier><identifier type="DOI">10.1002/(ISSN)1522-2616</identifier><identifier type="PublisherID">MANA</identifier><part><date>2006</date><detail type="volume"><caption>vol.</caption><number>279</number></detail><detail type="issue"><caption>no.</caption><number>7</number></detail><extent unit="pages"><start>699</start><end>704</end><total>6</total></extent></part></relatedItem><identifier type="istex">D1C051F864B94C046641727F04A19E45162E0EDF</identifier><identifier type="DOI">10.1002/mana.200310386</identifier><identifier type="ArticleID">MANA200310386</identifier><accessCondition type="use and reproduction" contentType="copyright">Copyright © 2006 WILEY‐VCH Verlag GmbH & Co. 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