Norm Attaining Arens Extensions on ℓ1
We study norm attaining properties of the Arens extensions of multilinear forms defined on Banach spaces. Among other related results, we construct a multilinear form on ℓ1 with the property that only some fixed Arens extensions determined a priori attain their norms. We also study when multilinear...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/315641 |
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| _version_ | 1832558289288691712 |
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| author | Javier Falcó Domingo García Manuel Maestre Pilar Rueda |
| author_facet | Javier Falcó Domingo García Manuel Maestre Pilar Rueda |
| author_sort | Javier Falcó |
| collection | DOAJ |
| description | We study norm attaining properties of the Arens extensions of multilinear forms defined on Banach spaces. Among other related results, we construct a multilinear form on ℓ1 with the property that only some fixed Arens extensions determined a priori attain their norms. We also study when multilinear forms can be approximated by ones with the property that only some of their Arens extensions attain their norms. |
| format | Article |
| id | doaj-art-0cc2a10103194862b56f4c8941e8d557 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0cc2a10103194862b56f4c8941e8d5572025-02-03T01:32:40ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/315641315641Norm Attaining Arens Extensions on ℓ1Javier Falcó0Domingo García1Manuel Maestre2Pilar Rueda3Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USADepartamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, Burjasot, 46100 Valencia, SpainDepartamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, Burjasot, 46100 Valencia, SpainDepartamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, Burjasot, 46100 Valencia, SpainWe study norm attaining properties of the Arens extensions of multilinear forms defined on Banach spaces. Among other related results, we construct a multilinear form on ℓ1 with the property that only some fixed Arens extensions determined a priori attain their norms. We also study when multilinear forms can be approximated by ones with the property that only some of their Arens extensions attain their norms.http://dx.doi.org/10.1155/2014/315641 |
| spellingShingle | Javier Falcó Domingo García Manuel Maestre Pilar Rueda Norm Attaining Arens Extensions on ℓ1 Abstract and Applied Analysis |
| title | Norm Attaining Arens Extensions on ℓ1 |
| title_full | Norm Attaining Arens Extensions on ℓ1 |
| title_fullStr | Norm Attaining Arens Extensions on ℓ1 |
| title_full_unstemmed | Norm Attaining Arens Extensions on ℓ1 |
| title_short | Norm Attaining Arens Extensions on ℓ1 |
| title_sort | norm attaining arens extensions on l1 |
| url | http://dx.doi.org/10.1155/2014/315641 |
| work_keys_str_mv | AT javierfalco normattainingarensextensionsonl1 AT domingogarcia normattainingarensextensionsonl1 AT manuelmaestre normattainingarensextensionsonl1 AT pilarrueda normattainingarensextensionsonl1 |