A propriedade de Bishop-Phelps-Bollobás
This work aims to study the Bishop-Phelps-Bollobás Theorem for operators between Banach spaces. We will show that the set of norm-attaining operators from $X$ to $Y$ is norm dense in $\mathcal{L}(X,Y)$ when $ Y$ has property $\beta$ for any Banach space $X$. We will see that the pair $(\ell_1,Y)$ ha...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Brasil |
| Institución: | Universidade Federal de Uberlândia (UFU) |
| Repositorio: | Repositório Institucional da UFU |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufu.br:123456789/37664 |
| Acceso en línea: | https://repositorio.ufu.br/handle/123456789/37664 http://doi.org/10.14393/ufu.di.2023.110 |
| Access Level: | acceso abierto |
| Palabra clave: | Teorema de Bishop-Phelps-Bollobás Operadores lineares que atingem a norma Propriedade $\beta$ Propriedade AHSP Bishop-Phelps-Bollobás theorem Norm-attaining linear operators Property $\beta$ Property AHSP CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE |
| Sumario: | This work aims to study the Bishop-Phelps-Bollobás Theorem for operators between Banach spaces. We will show that the set of norm-attaining operators from $X$ to $Y$ is norm dense in $\mathcal{L}(X,Y)$ when $ Y$ has property $\beta$ for any Banach space $X$. We will see that the pair $(\ell_1,Y)$ has the Bishop-Phelps-Bollobás property for operators if and only if the Banach space $Y$ has the property $AHSP$. Besides that, if $Y$ is a uniformly convex space, we will see that the pair $(\ell^n_\infty,Y)$ satisfies the Bishop-Phelps-Bollobás property for operators. Furthermore, we will show that if $X$ is a uniformly convex space, the pair $(X,Y)$ has the Bishop-Phelps-Bollobás property for operators for any Banach space $Y$. |
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