Null Sequences in Coechelon Spaces
Identifieur interne : 000B05 ( Istex/Corpus ); précédent : 000B04; suivant : 000B06Null Sequences in Coechelon Spaces
Auteurs : Susanne Dierolf ; Pawel Doma SkiSource :
- Mathematische Nachrichten [ 0025-584X ] ; 1997.
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Abstract
We prove that for any Köthe matrices a and b if T : λ1(α) → λ0(b) maps bounded sets into relatively compact sets, then T factorizes through a Fréchet Montel space. This is a consequence of a given description of those compact subsets in a coechelon space k∞(v) of type oo which are contained in an absolutely convex hull of a null sequence. An example of a compact set which is not of that form is given.
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DOI: 10.1002/mana.19971840107
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<titleGroup><title type="main" xml:lang="en">Null Sequences in Coechelon Spaces</title>
</titleGroup>
<creators><creator xml:id="au1" creatorRole="author" affiliationRef="#af1"><personName><givenNames>Susanne</givenNames>
<familyName>Dierolf</familyName>
</personName>
</creator>
<creator xml:id="au2" creatorRole="author" affiliationRef="#af1"><personName><givenNames>Pawel</givenNames>
<familyName>Domański</familyName>
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<affiliationGroup><affiliation xml:id="af1" countryCode="PL" type="organization"><unparsedAffiliation>FB IV Mathematik Universität Trier D–54286 Trier Germany Faculty of Mathematics and Computer Science A. Mickiewicz University id. Matejki 48/49 60–769 Poznań Poland</unparsedAffiliation>
</affiliation>
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<keywordGroup xml:lang="en" type="author"><keyword xml:id="kwd1">Montel operator</keyword>
<keyword xml:id="kwd2">Factorization</keyword>
<keyword xml:id="kwd3">coechelon space</keyword>
<keyword xml:id="kwd4">Kothe sequence space</keyword>
<keyword xml:id="kwd5">compact set</keyword>
<keyword xml:id="kwd6">Mackey completion</keyword>
</keywordGroup>
<abstractGroup><abstract type="main" xml:lang="de"><title type="main">Abstract</title>
<p>We prove that for any Köthe matrices a and <i>b</i>
if <i>T : λ</i>
<sub>1</sub>
(α) → λ<sub>0</sub>
(<i>b</i>
) maps bounded sets into relatively compact sets, then <i>T</i>
factorizes through a Fréchet Montel space. This is a consequence of a given description of those compact subsets in a coechelon space <i>k∞</i>
(<i>v</i>
) of type oo which are contained in an absolutely convex hull of a null sequence. An example of a compact set which is not of that form is given.</p>
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<name type="personal"><namePart type="given">Susanne</namePart>
<namePart type="family">Dierolf</namePart>
<affiliation>FB IV Mathematik Universität Trier D–54286 Trier Germany Faculty of Mathematics and Computer Science A. Mickiewicz University id. Matejki 48/49 60–769 Poznań Poland</affiliation>
<role><roleTerm type="text">author</roleTerm>
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</name>
<name type="personal"><namePart type="given">Pawel</namePart>
<namePart type="family">Domański</namePart>
<affiliation>FB IV Mathematik Universität Trier D–54286 Trier Germany Faculty of Mathematics and Computer Science A. Mickiewicz University id. Matejki 48/49 60–769 Poznań Poland</affiliation>
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<originInfo><publisher>WILEY‐VCH Verlag</publisher>
<place><placeTerm type="text">Berlin</placeTerm>
</place>
<dateIssued encoding="w3cdtf">1997</dateIssued>
<dateCaptured encoding="w3cdtf">1994-09-19</dateCaptured>
<copyrightDate encoding="w3cdtf">1997</copyrightDate>
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<language><languageTerm type="code" authority="rfc3066">en</languageTerm>
<languageTerm type="code" authority="iso639-2b">eng</languageTerm>
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<abstract lang="de">We prove that for any Köthe matrices a and b if T : λ1(α) → λ0(b) maps bounded sets into relatively compact sets, then T factorizes through a Fréchet Montel space. This is a consequence of a given description of those compact subsets in a coechelon space k∞(v) of type oo which are contained in an absolutely convex hull of a null sequence. An example of a compact set which is not of that form is given.</abstract>
<subject lang="en"><genre>keywords</genre>
<topic>Montel operator</topic>
<topic>Factorization</topic>
<topic>coechelon space</topic>
<topic>Kothe sequence space</topic>
<topic>compact set</topic>
<topic>Mackey completion</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>Article</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>1997</date>
<detail type="volume"><caption>vol.</caption>
<number>184</number>
</detail>
<detail type="issue"><caption>no.</caption>
<number>1</number>
</detail>
<extent unit="pages"><start>167</start>
<end>176</end>
<total>10</total>
</extent>
</part>
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<identifier type="DOI">10.1002/mana.19971840107</identifier>
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<accessCondition type="use and reproduction" contentType="copyright">Copyright © 1997 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim</accessCondition>
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