A propriedade de Bishop-Phelps-Bollobás

• Ano de defesa: 2023
• Autor(a) principal: Silva, André Luis Martins Tomaz da
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; Brasil; Programa de Pós-graduação em Matemática
• Palavras-chave em Português: 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
• Link de acesso: https://repositorio.ufu.br/handle/123456789/37664; http://doi.org/10.14393/ufu.di.2023.110

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 $Y$.