A note on a problem of Abramovich, Aliprantis and Burkinshaw
Let B and T be two positive operators on a Banach lattice such that B is compact-friendly and T is locally quasi-nilpotent. Introducing the concept of positive quasi-similarity, we prove that T has a non-trivial closed invariant subspace provided B is positively quasi-similar to T . This gives an af...
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| Veröffentlicht in: | Positivity : an international journal devoted to the theory and applications of positivity in analysis 2011-09, Vol.15 (3), p.473-480, Article 473 |
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| container_issue | 3 |
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| container_title | Positivity : an international journal devoted to the theory and applications of positivity in analysis |
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| creator | CAGLAR, Mert MISIRLIOGLU, Tunç |
| description | Let
B
and
T
be two positive operators on a Banach lattice such that
B
is compact-friendly and
T
is locally quasi-nilpotent. Introducing the concept of positive quasi-similarity, we prove that
T
has a non-trivial closed invariant subspace provided
B
is positively quasi-similar to
T
. This gives an affirmative answer to a problem of Abramovich, Aliprantis and Burkinshaw with the commutativity condition replaced by the positive quasi-similarity of the corresponding operators. The notion of strong compact-friendliness is also introduced and relevant facts about it are discussed. |
| doi_str_mv | 10.1007/s11117-010-0096-2 |
| format | Article |
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B
and
T
be two positive operators on a Banach lattice such that
B
is compact-friendly and
T
is locally quasi-nilpotent. Introducing the concept of positive quasi-similarity, we prove that
T
has a non-trivial closed invariant subspace provided
B
is positively quasi-similar to
T
. This gives an affirmative answer to a problem of Abramovich, Aliprantis and Burkinshaw with the commutativity condition replaced by the positive quasi-similarity of the corresponding operators. The notion of strong compact-friendliness is also introduced and relevant facts about it are discussed.</description><identifier>ISSN: 1385-1292</identifier><identifier>EISSN: 1572-9281</identifier><identifier>DOI: 10.1007/s11117-010-0096-2</identifier><language>eng</language><publisher>Basel: SP Birkhäuser Verlag Basel</publisher><subject>Banach spaces ; Calculus of Variations and Optimal Control; Optimization ; Commuting ; Econometrics ; Exact sciences and technology ; Fourier Analysis ; Functional analysis ; Lattice theory ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Operator Theory ; Potential Theory ; Sciences and techniques of general use ; Studies</subject><ispartof>Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2011-09, Vol.15 (3), p.473-480, Article 473</ispartof><rights>Springer Basel AG 2010</rights><rights>2015 INIST-CNRS</rights><rights>Springer Basel AG 2011</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c345t-bc8f71803fa98cbb75b6250cec0baad1b179ce00b20588084a64db3b029968da3</citedby><cites>FETCH-LOGICAL-c345t-bc8f71803fa98cbb75b6250cec0baad1b179ce00b20588084a64db3b029968da3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11117-010-0096-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11117-010-0096-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24493899$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>CAGLAR, Mert</creatorcontrib><creatorcontrib>MISIRLIOGLU, Tunç</creatorcontrib><title>A note on a problem of Abramovich, Aliprantis and Burkinshaw</title><title>Positivity : an international journal devoted to the theory and applications of positivity in analysis</title><addtitle>Positivity</addtitle><description>Let
B
and
T
be two positive operators on a Banach lattice such that
B
is compact-friendly and
T
is locally quasi-nilpotent. Introducing the concept of positive quasi-similarity, we prove that
T
has a non-trivial closed invariant subspace provided
B
is positively quasi-similar to
T
. This gives an affirmative answer to a problem of Abramovich, Aliprantis and Burkinshaw with the commutativity condition replaced by the positive quasi-similarity of the corresponding operators. The notion of strong compact-friendliness is also introduced and relevant facts about it are discussed.</description><subject>Banach spaces</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Commuting</subject><subject>Econometrics</subject><subject>Exact sciences and technology</subject><subject>Fourier Analysis</subject><subject>Functional analysis</subject><subject>Lattice theory</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operator Theory</subject><subject>Potential Theory</subject><subject>Sciences and techniques of general use</subject><subject>Studies</subject><issn>1385-1292</issn><issn>1572-9281</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp9UE1LxDAULKLguvoDvAXBm9GXtM0HeKmLXyB40XNI0tTN2m3XpKv4783SRUHQd3nvMDNvZrLsmMA5AeAXkaThGAhgAMkw3ckmpOQUSyrIbrpzUWJCJd3PDmJcQAJCAZPsskJdPzjUd0ijVehN65aob1Blgl72797Oz1DV-lXQ3eAj0l2Nrtbh1Xdxrj8Os71Gt9Edbfc0e765fprd4YfH2_tZ9YBtXpQDNlY0nAjIGy2FNYaXhtESrLNgtK6JIVxaB2AolEKAKDQrapMboFIyUet8mp2Musng29rFQS36dejSSyUEY4yzvEwgMoJs6GMMrlGr4Jc6fCoCatORGjtSKbradKRo4pxuhXW0um1SSuvjN5EWhcyFlAnHf2lbP-jB990QtG___UBHZkyi3YsLP9b_Jn0BfmaGUQ</recordid><startdate>20110901</startdate><enddate>20110901</enddate><creator>CAGLAR, Mert</creator><creator>MISIRLIOGLU, Tunç</creator><general>SP Birkhäuser Verlag Basel</general><general>Springer</general><general>Springer Nature B.V</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L6V</scope><scope>M0C</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20110901</creationdate><title>A note on a problem of Abramovich, Aliprantis and Burkinshaw</title><author>CAGLAR, Mert ; MISIRLIOGLU, Tunç</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c345t-bc8f71803fa98cbb75b6250cec0baad1b179ce00b20588084a64db3b029968da3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Banach spaces</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Commuting</topic><topic>Econometrics</topic><topic>Exact sciences and technology</topic><topic>Fourier Analysis</topic><topic>Functional analysis</topic><topic>Lattice theory</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operator Theory</topic><topic>Potential Theory</topic><topic>Sciences and techniques of general use</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>CAGLAR, Mert</creatorcontrib><creatorcontrib>MISIRLIOGLU, Tunç</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ABI/INFORM Global</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Positivity : an international journal devoted to the theory and applications of positivity in analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>CAGLAR, Mert</au><au>MISIRLIOGLU, Tunç</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A note on a problem of Abramovich, Aliprantis and Burkinshaw</atitle><jtitle>Positivity : an international journal devoted to the theory and applications of positivity in analysis</jtitle><stitle>Positivity</stitle><date>2011-09-01</date><risdate>2011</risdate><volume>15</volume><issue>3</issue><spage>473</spage><epage>480</epage><pages>473-480</pages><artnum>473</artnum><issn>1385-1292</issn><eissn>1572-9281</eissn><abstract>Let
B
and
T
be two positive operators on a Banach lattice such that
B
is compact-friendly and
T
is locally quasi-nilpotent. Introducing the concept of positive quasi-similarity, we prove that
T
has a non-trivial closed invariant subspace provided
B
is positively quasi-similar to
T
. This gives an affirmative answer to a problem of Abramovich, Aliprantis and Burkinshaw with the commutativity condition replaced by the positive quasi-similarity of the corresponding operators. The notion of strong compact-friendliness is also introduced and relevant facts about it are discussed.</abstract><cop>Basel</cop><pub>SP Birkhäuser Verlag Basel</pub><doi>10.1007/s11117-010-0096-2</doi><tpages>8</tpages></addata></record> |
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| ispartof | Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2011-09, Vol.15 (3), p.473-480, Article 473 |
| issn | 1385-1292 1572-9281 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings; EBSCOhost Business Source Complete |
| subjects | Banach spaces Calculus of Variations and Optimal Control Optimization Commuting Econometrics Exact sciences and technology Fourier Analysis Functional analysis Lattice theory Mathematical analysis Mathematics Mathematics and Statistics Operator Theory Potential Theory Sciences and techniques of general use Studies |
| title | A note on a problem of Abramovich, Aliprantis and Burkinshaw |
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