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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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><qualityIndicators><score>4.442</score><pdfVersion>1.3</pdfVersion><pdfPageSize>468 x 684 pts</pdfPageSize><refBibsNative>true</refBibsNative><abstractCharCount>404</abstractCharCount><pdfWordCount>3518</pdfWordCount><pdfCharCount>16314</pdfCharCount><pdfPageCount>10</pdfPageCount><abstractWordCount>77</abstractWordCount></qualityIndicators><title>Null Sequences in Coechelon Spaces</title><refBibs><json:item><host><pages><last>133</last><first>35</first></pages><author></author><title>Bierstedt, K. D.:An Introduction to Locally Convex Inductive Limits, in: Functional Analysis and Its Applications,World. Sci Publ.,Singapore,35–133(1988)</title></host></json:item><json:item><author><json:item><name>K. D. 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An example of a compact set which is not of that form is given.</p></abstract><textClass xml:lang="en"><keywords scheme="keyword"><list><head>keywords</head><item><term>Montel operator</term></item><item><term>Factorization</term></item><item><term>coechelon space</term></item><item><term>Kothe sequence space</term></item><item><term>compact set</term></item><item><term>Mackey completion</term></item></list></keywords></textClass><textClass><keywords scheme="Journal Subject"><list><head>article-category</head><item><term>Article</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="1994-09-19">Received</change><change when="1997">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/84CA64A5377599D5ACCA2C6BE54DB07B218873B3/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration><istex:document><component version="2.0" type="serialArticle" xml:lang="en"><header><publicationMeta level="product"><publisherInfo><publisherName>WILEY‐VCH Verlag</publisherName><publisherLoc>Berlin</publisherLoc></publisherInfo><doi registered="yes">10.1002/(ISSN)1522-2616</doi><issn type="print">0025-584X</issn><issn type="electronic">1522-2616</issn><idGroup><id type="product" value="MANA"></id></idGroup><titleGroup><title type="main" xml:lang="de" sort="MATHEMATISCHE NACHRICHTEN">Mathematische Nachrichten</title><title type="short">Math. 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Mickiewicz University id. Matejki 48/49 60–769 Poznań Poland</unparsedAffiliation></affiliation></affiliationGroup><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. 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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></relatedItem><identifier type="istex">84CA64A5377599D5ACCA2C6BE54DB07B218873B3</identifier><identifier type="DOI">10.1002/mana.19971840107</identifier><identifier type="ArticleID">MANA19971840107</identifier><accessCondition type="use and reproduction" contentType="copyright">Copyright © 1997 WILEY‐VCH Verlag GmbH & Co. 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