A note on strictly regular Fréchet spaces
Identifieur interne : 000910 ( Istex/Corpus ); précédent : 000909; suivant : 000911A note on strictly regular Fréchet spaces
Auteurs : S. Dierolf ; D. N. ZarnadzeSource :
- Archiv der Mathematik [ 0003-889X ] ; 1984-06-01.
Url:
DOI: 10.1007/BF01194053
Links to Exploration step
ISTEX:3C35CFBC88374DB0CADEE46B7EB829C167BAB85ALe document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">A note on strictly regular Fréchet spaces</title><author><name sortKey="Dierolf, S" sort="Dierolf, S" uniqKey="Dierolf S" first="S." last="Dierolf">S. Dierolf</name><affiliation><mods:affiliation>Fachbereich IV - Mathematik der Universität Trier, Postfach 38 25, D-5500, Trier</mods:affiliation></affiliation></author><author><name sortKey="Zarnadze, D N" sort="Zarnadze, D N" uniqKey="Zarnadze D" first="D. N." last="Zarnadze">D. N. Zarnadze</name><affiliation><mods:affiliation>Vychisl. Tsentr Akad Nauk Gruz. SSR, 380093, Tbilisi (Tiflis), UdSSR</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:3C35CFBC88374DB0CADEE46B7EB829C167BAB85A</idno><date when="1984" year="1984">1984</date><idno type="doi">10.1007/BF01194053</idno><idno type="url">https://api.istex.fr/document/3C35CFBC88374DB0CADEE46B7EB829C167BAB85A/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000910</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000910</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">A note on strictly regular Fréchet spaces</title><author><name sortKey="Dierolf, S" sort="Dierolf, S" uniqKey="Dierolf S" first="S." last="Dierolf">S. Dierolf</name><affiliation><mods:affiliation>Fachbereich IV - Mathematik der Universität Trier, Postfach 38 25, D-5500, Trier</mods:affiliation></affiliation></author><author><name sortKey="Zarnadze, D N" sort="Zarnadze, D N" uniqKey="Zarnadze D" first="D. N." last="Zarnadze">D. N. Zarnadze</name><affiliation><mods:affiliation>Vychisl. Tsentr Akad Nauk Gruz. SSR, 380093, Tbilisi (Tiflis), UdSSR</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Archiv der Mathematik</title><title level="j" type="abbrev">Arch. Math</title><idno type="ISSN">0003-889X</idno><idno type="eISSN">1420-8938</idno><imprint><publisher>Birkhäuser-Verlag</publisher><pubPlace>Basel</pubPlace><date type="published" when="1984-06-01">1984-06-01</date><biblScope unit="volume">42</biblScope><biblScope unit="issue">6</biblScope><biblScope unit="page" from="549">549</biblScope><biblScope unit="page" to="556">556</biblScope></imprint><idno type="ISSN">0003-889X</idno></series><idno type="istex">3C35CFBC88374DB0CADEE46B7EB829C167BAB85A</idno><idno type="DOI">10.1007/BF01194053</idno><idno type="ArticleID">BF01194053</idno><idno type="ArticleID">Art13</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0003-889X</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader></TEI><istex><corpusName>springer</corpusName><author><json:item><name>S. Dierolf</name><affiliations><json:string>Fachbereich IV - Mathematik der Universität Trier, Postfach 38 25, D-5500, Trier</json:string></affiliations></json:item><json:item><name>D. N. Zarnadze</name><affiliations><json:string>Vychisl. Tsentr Akad Nauk Gruz. SSR, 380093, Tbilisi (Tiflis), UdSSR</json:string></affiliations></json:item></author><articleId><json:string>BF01194053</json:string><json:string>Art13</json:string></articleId><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><qualityIndicators><score>3.673</score><pdfVersion>1.3</pdfVersion><pdfPageSize>486 x 684 pts</pdfPageSize><refBibsNative>false</refBibsNative><keywordCount>0</keywordCount><abstractCharCount>0</abstractCharCount><pdfWordCount>3661</pdfWordCount><pdfCharCount>16533</pdfCharCount><pdfPageCount>8</pdfPageCount><abstractWordCount>1</abstractWordCount></qualityIndicators><title>A note on strictly regular Fréchet spaces</title><refBibs><json:item><author><json:item><name>S,F Bellenot</name></json:item><json:item><name>E Dubinsky</name></json:item></author><host><volume>273</volume><pages><last>594</last><first>579</first></pages><author></author><title>Trans. Amer. Math. Soc</title><publicationDate>1982</publicationDate></host><title>Fr6chet spaces with nuclear K6the quotients</title><publicationDate>1982</publicationDate></json:item><json:item><author><json:item><name>J Diestel</name></json:item></author><host><volume>485</volume><author></author><title>LNM</title><publicationDate>1975</publicationDate></host><title>Geometry of Banach Spaces -Selected Topics</title><publicationDate>1975</publicationDate></json:item><json:item><author><json:item><name>V Eberhardt</name></json:item><json:item><name>Beispiele Vektorrfiume Mit Der Komplementfirraumeigenschaft</name></json:item></author><host><volume>26</volume><pages><last>636</last><first>627</first></pages><author></author><title>Arch. Math</title><publicationDate>1975</publicationDate></host><publicationDate>1975</publicationDate></json:item><json:item><author><json:item><name>A Grothendieck</name></json:item></author><host><pages><last>123</last><first>57</first></pages><author></author><title>Sur les espaces (F) et (DF). Summa Brasil</title><publicationDate>1954</publicationDate></host><publicationDate>1954</publicationDate></json:item><json:item><author><json:item><name>J Horvath</name></json:item></author><host><author></author><title>Topological Vector Spaces and Distributions</title><publicationDate>1966</publicationDate></host><publicationDate>1966</publicationDate></json:item><json:item><host><author><json:item><name>G Kt~the</name></json:item></author><title>Topological vector spaces I</title><publicationDate>1969</publicationDate></host></json:item><json:item><author><json:item><name>V,B Moscatelli</name></json:item></author><host><pages><last>66</last><first>63</first></pages><author></author><title>Fr6chet spaces without continuous norms and without bases</title><publicationDate>1980</publicationDate></host><publicationDate>1980</publicationDate></json:item><json:item><author><json:item><name>R,R Phelps</name></json:item></author><host><volume>8</volume><pages><last>450</last><first>444</first></pages><author></author><title>Arch. Math</title><publicationDate>1957</publicationDate></host><title>Subreflexive normed linear spaces</title><publicationDate>1957</publicationDate></json:item><json:item><author><json:item><name>W Slowikowski</name></json:item><json:item><name>W Zawadowskx</name></json:item></author><host><volume>15</volume><pages><last>272</last><first>267</first></pages><author></author><title>Studia Math</title><publicationDate>1956</publicationDate></host><title>Note on relatively complete Bo-spaces</title><publicationDate>1956</publicationDate></json:item><json:item><author><json:item><name>D,N Zarnadze</name></json:item></author><host><volume>19</volume><pages><last>40</last><first>29</first></pages><issue>1</issue><author></author><title>Tr. Vychisl. Tsentr. Akad. Nauk Gruz. SSR</title><publicationDate>1979</publicationDate></host><title>On certain locally convex spaces of continuous functions and Radon measures</title><publicationDate>1979</publicationDate></json:item><json:item><author><json:item><name>D,N Zarnadze</name></json:item></author><host><volume>44</volume><pages><last>830</last><first>821</first></pages><author></author><title>Izvestija Akad. Nauk SSR</title><publicationDate>1980</publicationDate></host><title>Reflexivity and best approximation in Fr6chet spaces</title><publicationDate>1980</publicationDate></json:item><json:item><author><json:item><name>D,N Zarnadze</name></json:item></author><host><volume>31</volume><pages><last>458</last><first>454</first></pages><issue>6</issue><author></author><title>Math. Notes</title><publicationDate>1982</publicationDate></host><title>Strictly regular Fr+chet spaces</title><publicationDate>1982</publicationDate></json:item><json:item><host><author><json:item><name>D,N Zarnadze</name></json:item></author><title>Reflexivity and the supremum of linear continuous functionals in Fr6chet spaces. To appear in Funkts. Analiz i Prilozh</title><publicationDate>1983</publicationDate></host></json:item><json:item><author><json:item><name>N David</name></json:item><json:item><name> Vychisl</name></json:item></author><host><author></author><title>Tsentr Akad Nauk Gruz. SSR 380093 Tbitisi</title></host></json:item></refBibs><genre><json:string>research-article</json:string></genre><host><volume>42</volume><pages><last>556</last><first>549</first></pages><issn><json:string>0003-889X</json:string></issn><issue>6</issue><subject><json:item><value>Mathematics, general</value></json:item></subject><journalId><json:string>13</json:string></journalId><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1420-8938</json:string></eissn><title>Archiv der Mathematik</title><publicationDate>1984</publicationDate><copyrightDate>1984</copyrightDate></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>1984</publicationDate><copyrightDate>1984</copyrightDate><doi><json:string>10.1007/BF01194053</json:string></doi><id>3C35CFBC88374DB0CADEE46B7EB829C167BAB85A</id><score>0.47411293</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/3C35CFBC88374DB0CADEE46B7EB829C167BAB85A/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/3C35CFBC88374DB0CADEE46B7EB829C167BAB85A/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/3C35CFBC88374DB0CADEE46B7EB829C167BAB85A/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">A note on strictly regular Fréchet spaces</title><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>Birkhäuser-Verlag</publisher><pubPlace>Basel</pubPlace><availability><p>Birkhäuser Verlag, 1984</p></availability><date>1983-08-29</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">A note on strictly regular Fréchet spaces</title><author xml:id="author-1"><persName><forename type="first">S.</forename><surname>Dierolf</surname></persName><affiliation>Fachbereich IV - Mathematik der Universität Trier, Postfach 38 25, D-5500, Trier</affiliation></author><author xml:id="author-2"><persName><forename type="first">D.</forename><surname>Zarnadze</surname></persName><affiliation>Vychisl. Tsentr Akad Nauk Gruz. SSR, 380093, Tbilisi (Tiflis), UdSSR</affiliation></author></analytic><monogr><title level="j">Archiv der Mathematik</title><title level="j" type="abbrev">Arch. Math</title><idno type="journal-ID">13</idno><idno type="pISSN">0003-889X</idno><idno type="eISSN">1420-8938</idno><idno type="issue-article-count">17</idno><idno type="volume-issue-count">6</idno><imprint><publisher>Birkhäuser-Verlag</publisher><pubPlace>Basel</pubPlace><date type="published" when="1984-06-01"></date><biblScope unit="volume">42</biblScope><biblScope unit="issue">6</biblScope><biblScope unit="page" from="549">549</biblScope><biblScope unit="page" to="556">556</biblScope></imprint></monogr><idno type="istex">3C35CFBC88374DB0CADEE46B7EB829C167BAB85A</idno><idno type="DOI">10.1007/BF01194053</idno><idno type="ArticleID">BF01194053</idno><idno type="ArticleID">Art13</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>1983-08-29</date></creation><langUsage><language ident="en">en</language></langUsage><textClass><keywords scheme="Journal Subject"><list><head>Mathematics</head><item><term>Mathematics, general</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1983-08-29">Created</change><change when="1984-06-01">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2016-11-22">References added</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-01-20">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/3C35CFBC88374DB0CADEE46B7EB829C167BAB85A/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Springer, Publisher found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType><istex:document><Publisher><PublisherInfo><PublisherName>Birkhäuser-Verlag</PublisherName><PublisherLocation>Basel</PublisherLocation></PublisherInfo><Journal><JournalInfo JournalProductType="ArchiveJournal" NumberingStyle="Unnumbered"><JournalID>13</JournalID><JournalPrintISSN>0003-889X</JournalPrintISSN><JournalElectronicISSN>1420-8938</JournalElectronicISSN><JournalTitle>Archiv der Mathematik</JournalTitle><JournalAbbreviatedTitle>Arch. Math</JournalAbbreviatedTitle><JournalSubjectGroup><JournalSubject Type="Primary">Mathematics</JournalSubject><JournalSubject Type="Secondary">Mathematics, general</JournalSubject></JournalSubjectGroup></JournalInfo><Volume><VolumeInfo VolumeType="Regular" TocLevels="0"><VolumeIDStart>42</VolumeIDStart><VolumeIDEnd>42</VolumeIDEnd><VolumeIssueCount>6</VolumeIssueCount></VolumeInfo><Issue IssueType="Regular"><IssueInfo TocLevels="0"><IssueIDStart>6</IssueIDStart><IssueIDEnd>6</IssueIDEnd><IssueArticleCount>17</IssueArticleCount><IssueHistory><CoverDate><DateString>1. 6. 1984</DateString><Year>1984</Year><Month>6</Month></CoverDate></IssueHistory><IssueCopyright><CopyrightHolderName>Birkhäuser Verlag</CopyrightHolderName><CopyrightYear>1984</CopyrightYear></IssueCopyright></IssueInfo><Article ID="Art13"><ArticleInfo Language="En" ArticleType="OriginalPaper" NumberingStyle="Unnumbered" TocLevels="0" ContainsESM="No"><ArticleID>BF01194053</ArticleID><ArticleDOI>10.1007/BF01194053</ArticleDOI><ArticleSequenceNumber>13</ArticleSequenceNumber><ArticleTitle Language="En">A note on strictly regular Fréchet spaces</ArticleTitle><ArticleFirstPage>549</ArticleFirstPage><ArticleLastPage>556</ArticleLastPage><ArticleHistory><RegistrationDate><Year>2005</Year><Month>2</Month><Day>4</Day></RegistrationDate><Received><Year>1983</Year><Month>8</Month><Day>29</Day></Received></ArticleHistory><ArticleCopyright><CopyrightHolderName>Birkhäuser Verlag</CopyrightHolderName><CopyrightYear>1984</CopyrightYear></ArticleCopyright><ArticleGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ArticleGrants><ArticleContext><JournalID>13</JournalID><VolumeIDStart>42</VolumeIDStart><VolumeIDEnd>42</VolumeIDEnd><IssueIDStart>6</IssueIDStart><IssueIDEnd>6</IssueIDEnd></ArticleContext></ArticleInfo><ArticleHeader><AuthorGroup><Author AffiliationIDS="Aff1" PresentAffiliationID="Aff1"><AuthorName DisplayOrder="Western"><GivenName>S.</GivenName><FamilyName>Dierolf</FamilyName></AuthorName></Author><Author AffiliationIDS="Aff2" PresentAffiliationID="Aff2"><AuthorName DisplayOrder="Western"><GivenName>D.</GivenName><GivenName>N.</GivenName><FamilyName>Zarnadze</FamilyName></AuthorName></Author><Affiliation ID="Aff1"><OrgName>Fachbereich IV - Mathematik der Universität Trier</OrgName><OrgAddress><Postbox>Postfach 38 25</Postbox><Postcode>D-5500</Postcode><City>Trier</City></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgName>Vychisl. Tsentr Akad Nauk Gruz. SSR</OrgName><OrgAddress><Postcode>380093</Postcode><City>Tbilisi (Tiflis)</City><Country>UdSSR</Country></OrgAddress></Affiliation></AuthorGroup><ArticleNote Type="ProofNote"><SimplePara>It was V. B. Moscatelli [7] who showed that the class of strictly regular Fréchet spaces is not trivial i.e. does not consist of countable products of Banach spaces only. Recently this class has gained additional interest by a result of K. Floret and V. B. Moscatelli (On bases in strict inductive and projective limits of locally convex spaces, preprint 1983), who proved that a reflexive strictly regular Fréchet space admits an unconditional basis if and only if it is isomorphic to a product of Banach spaces each admitting an unconditional basis.</SimplePara><SimplePara>Furthermore, it should be mentioned that the Propositions 3 and 4 of the above note have their roots in the following two articles</SimplePara><SimplePara>K.<Emphasis Type="SmallCaps">Floret</Emphasis> and M.<Emphasis Type="SmallCaps">Wriedt</Emphasis>, Reflexivität und Bestapproximation in Fréchet-Räumen. Arch. Math.<Emphasis Type="Bold">23</Emphasis>, 70–72 (1972);</SimplePara><SimplePara>M.<Emphasis Type="SmallCaps">Wriedt</Emphasis>, Beiträge zur Approximationstheorie in metrisierbaren lokalkonvexen Räumen. Math. Nachr.<Emphasis Type="Bold">64</Emphasis>, 135–147(1974).</SimplePara></ArticleNote></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A note on strictly regular Fréchet spaces</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>A note on strictly regular Fréchet spaces</title></titleInfo><name type="personal"><namePart type="given">S.</namePart><namePart type="family">Dierolf</namePart><affiliation>Fachbereich IV - Mathematik der Universität Trier, Postfach 38 25, D-5500, Trier</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">D.</namePart><namePart type="given">N.</namePart><namePart type="family">Zarnadze</namePart><affiliation>Vychisl. Tsentr Akad Nauk Gruz. SSR, 380093, Tbilisi (Tiflis), UdSSR</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper"></genre><originInfo><publisher>Birkhäuser-Verlag</publisher><place><placeTerm type="text">Basel</placeTerm></place><dateCreated encoding="w3cdtf">1983-08-29</dateCreated><dateIssued encoding="w3cdtf">1984-06-01</dateIssued><copyrightDate encoding="w3cdtf">1984</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><relatedItem type="host"><titleInfo><title>Archiv der Mathematik</title></titleInfo><titleInfo type="abbreviated"><title>Arch. Math</title></titleInfo><genre type="journal" displayLabel="Archive Journal"></genre><originInfo><dateIssued encoding="w3cdtf">1984-06-01</dateIssued><copyrightDate encoding="w3cdtf">1984</copyrightDate></originInfo><subject><genre>Mathematics</genre><topic>Mathematics, general</topic></subject><identifier type="ISSN">0003-889X</identifier><identifier type="eISSN">1420-8938</identifier><identifier type="JournalID">13</identifier><identifier type="IssueArticleCount">17</identifier><identifier type="VolumeIssueCount">6</identifier><part><date>1984</date><detail type="volume"><number>42</number><caption>vol.</caption></detail><detail type="issue"><number>6</number><caption>no.</caption></detail><extent unit="pages"><start>549</start><end>556</end></extent></part><recordInfo><recordOrigin>Birkhäuser Verlag, 1984</recordOrigin></recordInfo></relatedItem><identifier type="istex">3C35CFBC88374DB0CADEE46B7EB829C167BAB85A</identifier><identifier type="DOI">10.1007/BF01194053</identifier><identifier type="ArticleID">BF01194053</identifier><identifier type="ArticleID">Art13</identifier><accessCondition type="use and reproduction" contentType="copyright">Birkhäuser Verlag, 1984</accessCondition><recordInfo><recordContentSource>SPRINGER</recordContentSource><recordOrigin>Birkhäuser Verlag, 1984</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Rhénanie/explor/UnivTrevesV1/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000910 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 000910 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Rhénanie
|area= UnivTrevesV1
|flux= Istex
|étape= Corpus
|type= RBID
|clé= ISTEX:3C35CFBC88374DB0CADEE46B7EB829C167BAB85A
|texte= A note on strictly regular Fréchet spaces
}}
| This area was generated with Dilib version V0.6.31. |  |