On uniqueness and plentitude of subsymmetric sequences
We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization Su( T *) of Tsirelson’s original Banach space provides the first known example of a space with a unique subsymmetric basic sequence that is additionally non-symmetric. Co...
Gespeichert in:
| Veröffentlicht in: | Israel journal of mathematics 2024-06, Vol.261 (2), p.613-636 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 636 |
|---|---|
| container_issue | 2 |
| container_start_page | 613 |
| container_title | Israel journal of mathematics |
| container_volume | 261 |
| creator | Casazza, Peter G. Dilworth, Stephen J. Kutzarova, Denka Motakis, Pavlos |
| description | We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization Su(
T
*) of Tsirelson’s original Banach space provides the first known example of a space with a unique subsymmetric basic sequence that is additionally non-symmetric. Contrastingly, we provide a criterion for a space with a sub-symmetric basis to contain a continuum of nonequivalent subsymmetric basic sequences and apply it to Su(
T
*)*. Finally, we provide a criterion for a subsymmetric sequence to be equivalent to the unit vector basis of some
ℓ
p
or
c
0
. |
| doi_str_mv | 10.1007/s11856-023-2589-2 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3082954892</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3082954892</sourcerecordid><originalsourceid>FETCH-LOGICAL-c268t-351cd29f0f39b4959994e8e939c0b2a3505982b6dd5de02ddcff01e9220a75a73</originalsourceid><addsrcrecordid>eNp1kD1PwzAURS0EEqXwA9giMRuen-vEHlEFFKlSF5itxB8oVesUv2TovydRkJiY7nLuvdJh7F7AowConkgIrUoOKDkqbThesIVQpeJaCXHJFgAoOIoKr9kN0R5AyUrIBSt3qRhS-z2EFIiKOvnidAipb_vBh6KLBQ0NnY_H0OfWFRQm0AW6ZVexPlC4-80l-3x9-Vhv-Hb39r5-3nKHpe65VMJ5NBGiNM3KKGPMKuhgpHHQYC0VKKOxKb1XPgB672IEEQwi1JWqK7lkD_PuKXfjNfV23w05jZdWgkajVtrgSImZcrkjyiHaU26PdT5bAXbSY2c9dtRjJz126uDcoZFNXyH_Lf9f-gFDoGc3</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3082954892</pqid></control><display><type>article</type><title>On uniqueness and plentitude of subsymmetric sequences</title><source>SpringerLink Journals - AutoHoldings</source><creator>Casazza, Peter G. ; Dilworth, Stephen J. ; Kutzarova, Denka ; Motakis, Pavlos</creator><creatorcontrib>Casazza, Peter G. ; Dilworth, Stephen J. ; Kutzarova, Denka ; Motakis, Pavlos</creatorcontrib><description>We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization Su(
T
*) of Tsirelson’s original Banach space provides the first known example of a space with a unique subsymmetric basic sequence that is additionally non-symmetric. Contrastingly, we provide a criterion for a space with a sub-symmetric basis to contain a continuum of nonequivalent subsymmetric basic sequences and apply it to Su(
T
*)*. Finally, we provide a criterion for a subsymmetric sequence to be equivalent to the unit vector basis of some
ℓ
p
or
c
0
.</description><identifier>ISSN: 0021-2172</identifier><identifier>EISSN: 1565-8511</identifier><identifier>DOI: 10.1007/s11856-023-2589-2</identifier><language>eng</language><publisher>Jerusalem: The Hebrew University Magnes Press</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Banach spaces ; Criteria ; Group Theory and Generalizations ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Theoretical</subject><ispartof>Israel journal of mathematics, 2024-06, Vol.261 (2), p.613-636</ispartof><rights>The Hebrew University of Jerusalem 2023</rights><rights>The Hebrew University of Jerusalem 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-351cd29f0f39b4959994e8e939c0b2a3505982b6dd5de02ddcff01e9220a75a73</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/s11856-023-2589-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11856-023-2589-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Casazza, Peter G.</creatorcontrib><creatorcontrib>Dilworth, Stephen J.</creatorcontrib><creatorcontrib>Kutzarova, Denka</creatorcontrib><creatorcontrib>Motakis, Pavlos</creatorcontrib><title>On uniqueness and plentitude of subsymmetric sequences</title><title>Israel journal of mathematics</title><addtitle>Isr. J. Math</addtitle><description>We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization Su(
T
*) of Tsirelson’s original Banach space provides the first known example of a space with a unique subsymmetric basic sequence that is additionally non-symmetric. Contrastingly, we provide a criterion for a space with a sub-symmetric basis to contain a continuum of nonequivalent subsymmetric basic sequences and apply it to Su(
T
*)*. Finally, we provide a criterion for a subsymmetric sequence to be equivalent to the unit vector basis of some
ℓ
p
or
c
0
.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Banach spaces</subject><subject>Criteria</subject><subject>Group Theory and Generalizations</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Theoretical</subject><issn>0021-2172</issn><issn>1565-8511</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp1kD1PwzAURS0EEqXwA9giMRuen-vEHlEFFKlSF5itxB8oVesUv2TovydRkJiY7nLuvdJh7F7AowConkgIrUoOKDkqbThesIVQpeJaCXHJFgAoOIoKr9kN0R5AyUrIBSt3qRhS-z2EFIiKOvnidAipb_vBh6KLBQ0NnY_H0OfWFRQm0AW6ZVexPlC4-80l-3x9-Vhv-Hb39r5-3nKHpe65VMJ5NBGiNM3KKGPMKuhgpHHQYC0VKKOxKb1XPgB672IEEQwi1JWqK7lkD_PuKXfjNfV23w05jZdWgkajVtrgSImZcrkjyiHaU26PdT5bAXbSY2c9dtRjJz126uDcoZFNXyH_Lf9f-gFDoGc3</recordid><startdate>20240601</startdate><enddate>20240601</enddate><creator>Casazza, Peter G.</creator><creator>Dilworth, Stephen J.</creator><creator>Kutzarova, Denka</creator><creator>Motakis, Pavlos</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240601</creationdate><title>On uniqueness and plentitude of subsymmetric sequences</title><author>Casazza, Peter G. ; Dilworth, Stephen J. ; Kutzarova, Denka ; Motakis, Pavlos</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-351cd29f0f39b4959994e8e939c0b2a3505982b6dd5de02ddcff01e9220a75a73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Banach spaces</topic><topic>Criteria</topic><topic>Group Theory and Generalizations</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Casazza, Peter G.</creatorcontrib><creatorcontrib>Dilworth, Stephen J.</creatorcontrib><creatorcontrib>Kutzarova, Denka</creatorcontrib><creatorcontrib>Motakis, Pavlos</creatorcontrib><collection>CrossRef</collection><jtitle>Israel journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Casazza, Peter G.</au><au>Dilworth, Stephen J.</au><au>Kutzarova, Denka</au><au>Motakis, Pavlos</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On uniqueness and plentitude of subsymmetric sequences</atitle><jtitle>Israel journal of mathematics</jtitle><stitle>Isr. J. Math</stitle><date>2024-06-01</date><risdate>2024</risdate><volume>261</volume><issue>2</issue><spage>613</spage><epage>636</epage><pages>613-636</pages><issn>0021-2172</issn><eissn>1565-8511</eissn><abstract>We explore the diversity of subsymmetric basic sequences in spaces with a subsymmetric basis. We prove that the subsymmetrization Su(
T
*) of Tsirelson’s original Banach space provides the first known example of a space with a unique subsymmetric basic sequence that is additionally non-symmetric. Contrastingly, we provide a criterion for a space with a sub-symmetric basis to contain a continuum of nonequivalent subsymmetric basic sequences and apply it to Su(
T
*)*. Finally, we provide a criterion for a subsymmetric sequence to be equivalent to the unit vector basis of some
ℓ
p
or
c
0
.</abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11856-023-2589-2</doi><tpages>24</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-2172 |
| ispartof | Israel journal of mathematics, 2024-06, Vol.261 (2), p.613-636 |
| issn | 0021-2172 1565-8511 |
| language | eng |
| recordid | cdi_proquest_journals_3082954892 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Analysis Applications of Mathematics Banach spaces Criteria Group Theory and Generalizations Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical |
| title | On uniqueness and plentitude of subsymmetric sequences |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-07T00%3A09%3A04IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20uniqueness%20and%20plentitude%20of%20subsymmetric%20sequences&rft.jtitle=Israel%20journal%20of%20mathematics&rft.au=Casazza,%20Peter%20G.&rft.date=2024-06-01&rft.volume=261&rft.issue=2&rft.spage=613&rft.epage=636&rft.pages=613-636&rft.issn=0021-2172&rft.eissn=1565-8511&rft_id=info:doi/10.1007/s11856-023-2589-2&rft_dat=%3Cproquest_cross%3E3082954892%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3082954892&rft_id=info:pmid/&rfr_iscdi=true |