The Fixed Point Property in c0 with an Equivalent Norm
We study the fixed point property (FPP) in the Banach space c0 with the equivalent norm ‖⋅‖D. The space c0 with this norm has the weak fixed point property. We prove that every infinite-dimensional subspace of (c0,‖⋅‖D) contains a complemented asymptotically isometric copy of c0, and thus does not h...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/574614 |
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| author | Berta Gamboa de Buen Fernando Núñez-Medina |
| author_facet | Berta Gamboa de Buen Fernando Núñez-Medina |
| author_sort | Berta Gamboa de Buen |
| collection | DOAJ |
| description | We study the fixed point property (FPP) in the Banach space c0 with the equivalent norm ‖⋅‖D. The space c0 with this norm has the weak fixed point property. We prove that every infinite-dimensional subspace of (c0,‖⋅‖D) contains a complemented asymptotically isometric copy of c0, and thus does not have the FPP, but there exist nonempty closed convex and bounded subsets of (c0,‖⋅‖D) which are not ω-compact and do not contain asymptotically isometric c0—summing basis sequences. Then we define a family of sequences which are asymptotically isometric to different bases equivalent to the summing basis in the space (c0,‖⋅‖D), and we give some of its properties. We also prove that the dual space of (c0,‖⋅‖D) over the reals is the Bynum space l1∞ and that every infinite-dimensional subspace of l1∞ does not have the fixed point property. |
| format | Article |
| id | doaj-art-bb7c97c85b294f9f83df958551216280 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bb7c97c85b294f9f83df9585512162802025-02-03T01:27:48ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/574614574614The Fixed Point Property in c0 with an Equivalent NormBerta Gamboa de Buen0Fernando Núñez-Medina1Matemáticas Básicas, Centro de Investigación en Matemáticas (CIMAT), Apartado Postal 402, 36000 Guanajuato, GTO, MexicoDepartamento de Matemáticas Aplicadas, Universidad del Papaloapan (UNPA), 68400 Loma Bonita, OAX, MexicoWe study the fixed point property (FPP) in the Banach space c0 with the equivalent norm ‖⋅‖D. The space c0 with this norm has the weak fixed point property. We prove that every infinite-dimensional subspace of (c0,‖⋅‖D) contains a complemented asymptotically isometric copy of c0, and thus does not have the FPP, but there exist nonempty closed convex and bounded subsets of (c0,‖⋅‖D) which are not ω-compact and do not contain asymptotically isometric c0—summing basis sequences. Then we define a family of sequences which are asymptotically isometric to different bases equivalent to the summing basis in the space (c0,‖⋅‖D), and we give some of its properties. We also prove that the dual space of (c0,‖⋅‖D) over the reals is the Bynum space l1∞ and that every infinite-dimensional subspace of l1∞ does not have the fixed point property.http://dx.doi.org/10.1155/2011/574614 |
| spellingShingle | Berta Gamboa de Buen Fernando Núñez-Medina The Fixed Point Property in c0 with an Equivalent Norm Abstract and Applied Analysis |
| title | The Fixed Point Property in c0 with an Equivalent Norm |
| title_full | The Fixed Point Property in c0 with an Equivalent Norm |
| title_fullStr | The Fixed Point Property in c0 with an Equivalent Norm |
| title_full_unstemmed | The Fixed Point Property in c0 with an Equivalent Norm |
| title_short | The Fixed Point Property in c0 with an Equivalent Norm |
| title_sort | fixed point property in c0 with an equivalent norm |
| url | http://dx.doi.org/10.1155/2011/574614 |
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