Ideais injetivos e sobrejetivos de polinômios homogêneos entre espaços de Banach

• Ano de defesa: 2021
• Autor(a) principal: Bazán, Pedro Manuel Contreras
• 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: espaços de Banach; Banach spaces; polinômios homogêneos; homogeneous polynomials; ideais de polinômios; polynomial ideals; ideais de composição; composition ideals; ideais injetivos; injective ideals; ideais sobrejetivos; surjective ideals; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE
• Link de acesso: https://repositorio.ufu.br/handle/123456789/32506; http://doi.org/10.14393/ufu.di.2021.276

The main purpose of this dissertation is to study injective and surjective ideals of homogeneous polynomials between Banach spaces. First we briefly sketch the theory of homogeneous polynomials and polynomial ideals. Next we study the spaces $\ell_\infty(\Gamma)$ and $\ell_1(\Gamma)$, formed by scalar families indexed by an arbitrary non void set $\Gamma$ endowed with the supremum norm and the sum norm, respectively, as well as metric injections and surjections and extension and lifting properties of such spaces. Then, injective polynomials ideals are investigated, with a special attention to the injective hull and to the description of the injective hull of a composition ideal. Finally we undertake a similar study concerning surjective polynomial ideals. Applications of the descriptions of the injective and surjective hulls of composition ideals are provided.