Espaços de operadores lineares, multilineares e polinômios regulares em espaços de Riesz e reticulados de Banach

• Ano de defesa: 2022
• Autor(a) principal: Monção, Ariel de Oliveira
• 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: espaço de Riesz; Dedekind completo; reticulado de Banach; operadores lineares regulares; operadores multilineares regulares; polinômios homogêneos regulares; norma regular; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::ANALISE FUNCIONAL; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::ANALISE FUNCIONAL NAO-LINEAR; Matemática; Análise funcional; Polinômios
• Link de acesso: https://repositorio.ufu.br/handle/123456789/35281; http://doi.org/10.14393/ufu.di.2022.228

The main purposes of this work are the following: (i) To show how an order relation can be introduced in the sets of regular linear operators, multilinear operators and homogeneous polynomials between Riesz spaces so that they become Riesz spaces. (ii) To show how a norm, called regular norm, can be defined in the spaces of regular linear operators, multilinear operators and homogeneous polynomials between Banach lattices so that they become Banach lattices. To achieve these tasks we prove, among several other results, the following fundamental theorems. The Kantorovich Theorem, which establishes that positive operators are fully determined by the positive cone of the domain space. The F. Riesz-Kantorovich Theorem, which guarantees that the space of regular linear operators taking values in a Dedekind complete space is a Dedekind complete Riesz space. And the result that assures that every positive linear operator from a Banach lattice to a normed Riesz space is continuous.