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Quotient Hereditarily Indecomposable Banach Spaces
A Banach space $X$ is said to be quotient hereditarily indecomposable if no infinite dimensional quotient of a subspace of $X$ is decomposable. We provide an example of a quotient hereditarily indecomposable space, namely the space ${{X}_{GM}}$ constructed by W. T. Gowers and B. Maurey in $[\text{GM...
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| Published in: | Canadian journal of mathematics 1999-06, Vol.51 (3), p.566-584 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c318t-f24c4569ee0b1228ab03985245ea9c3703606ece3a579dfbdc0a219833ffc143 |
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| cites | cdi_FETCH-LOGICAL-c318t-f24c4569ee0b1228ab03985245ea9c3703606ece3a579dfbdc0a219833ffc143 |
| container_end_page | 584 |
| container_issue | 3 |
| container_start_page | 566 |
| container_title | Canadian journal of mathematics |
| container_volume | 51 |
| creator | Ferenczi, V. |
| description | A Banach space
$X$
is said to be quotient hereditarily indecomposable if no infinite dimensional quotient of a subspace of
$X$
is decomposable. We provide an example of a quotient hereditarily indecomposable space, namely the space
${{X}_{GM}}$
constructed by W. T. Gowers and B. Maurey in
$[\text{GM}]$
. Then we provide an example of a reflexive hereditarily indecomposable space
$\hat{X}$
whose dual is not hereditarily indecomposable; so
$\hat{X}$
is not quotient hereditarily indecomposable. We also show that every operator on
${{\hat{X}}^{*}}$
is a strictly singular perturbation of an homothetic map. |
| doi_str_mv | 10.4153/CJM-1999-026-4 |
| format | article |
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$X$
is said to be quotient hereditarily indecomposable if no infinite dimensional quotient of a subspace of
$X$
is decomposable. We provide an example of a quotient hereditarily indecomposable space, namely the space
${{X}_{GM}}$
constructed by W. T. Gowers and B. Maurey in
$[\text{GM}]$
. Then we provide an example of a reflexive hereditarily indecomposable space
$\hat{X}$
whose dual is not hereditarily indecomposable; so
$\hat{X}$
is not quotient hereditarily indecomposable. We also show that every operator on
${{\hat{X}}^{*}}$
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$X$
is said to be quotient hereditarily indecomposable if no infinite dimensional quotient of a subspace of
$X$
is decomposable. We provide an example of a quotient hereditarily indecomposable space, namely the space
${{X}_{GM}}$
constructed by W. T. Gowers and B. Maurey in
$[\text{GM}]$
. Then we provide an example of a reflexive hereditarily indecomposable space
$\hat{X}$
whose dual is not hereditarily indecomposable; so
$\hat{X}$
is not quotient hereditarily indecomposable. We also show that every operator on
${{\hat{X}}^{*}}$
is a strictly singular perturbation of an homothetic map.</description><issn>0008-414X</issn><issn>1496-4279</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1999</creationdate><recordtype>article</recordtype><recordid>eNp1jztPwzAUhS0EEqGwMucPuPiVh0eogBYVIUQHNuvGuYZUeclOh_57HLUr07ln-K7OR8g9Z0vFM_mwenunXGtNmcipuiAJVzoeotCXJGGMlVRx9X1NbkLYxyrzjCdEfB6GqcF-StfosW4m8E17TDd9jXboxiFA1WL6BD3Y3_RrBIvhllw5aAPenXNBdi_Pu9Wabj9eN6vHLbWSlxN1QlmV5RqRVVyIEiomdZkJlSFoK4s4gOVoUUJW6NpVtWUguC6ldM5yJRdkeXpr_RCCR2dG33Tgj4YzMwubKGxmYROFzQywMwBd5Zv6B81-OPg-bvwP-QPdB1fR</recordid><startdate>19990601</startdate><enddate>19990601</enddate><creator>Ferenczi, V.</creator><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19990601</creationdate><title>Quotient Hereditarily Indecomposable Banach Spaces</title><author>Ferenczi, V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c318t-f24c4569ee0b1228ab03985245ea9c3703606ece3a579dfbdc0a219833ffc143</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1999</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ferenczi, V.</creatorcontrib><collection>CrossRef</collection><jtitle>Canadian journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ferenczi, V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quotient Hereditarily Indecomposable Banach Spaces</atitle><jtitle>Canadian journal of mathematics</jtitle><addtitle>Can. j. math</addtitle><date>1999-06-01</date><risdate>1999</risdate><volume>51</volume><issue>3</issue><spage>566</spage><epage>584</epage><pages>566-584</pages><issn>0008-414X</issn><eissn>1496-4279</eissn><abstract>A Banach space
$X$
is said to be quotient hereditarily indecomposable if no infinite dimensional quotient of a subspace of
$X$
is decomposable. We provide an example of a quotient hereditarily indecomposable space, namely the space
${{X}_{GM}}$
constructed by W. T. Gowers and B. Maurey in
$[\text{GM}]$
. Then we provide an example of a reflexive hereditarily indecomposable space
$\hat{X}$
whose dual is not hereditarily indecomposable; so
$\hat{X}$
is not quotient hereditarily indecomposable. We also show that every operator on
${{\hat{X}}^{*}}$
is a strictly singular perturbation of an homothetic map.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.4153/CJM-1999-026-4</doi><tpages>19</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0008-414X |
| ispartof | Canadian journal of mathematics, 1999-06, Vol.51 (3), p.566-584 |
| issn | 0008-414X 1496-4279 |
| language | eng |
| recordid | cdi_crossref_primary_10_4153_CJM_1999_026_4 |
| source | Freely Accessible Science Journals - check A-Z of ejournals |
| title | Quotient Hereditarily Indecomposable Banach Spaces |
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