Espaços de sequências vetoriais e ideais de operadores

• Autor(a) principal: Nogueira, Davidson Freitas
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFU
• Texto Completo: https://repositorio.ufu.br/handle/123456789/16827; http://doi.org/10.14393/ufu.di.2016.128
• topic: Banach, Espaços de; Sequências (Matemática); Operadores lineares; Análise funcional; Análise matemática; Espaços de Banach; Espaços de sequências; Ideais de operadores; Sequências absolutamente somáveis; Sequências fracamente somáveis; Sequências fracamente nulas; Operadores somantes; Banach spaces; Sequence spaces; Operator ideals; Strongly summable sequences; Weakly summable sequences; Weakly null sequences; Summing operators; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The main purpose of this dissertation is the study of ideals of operators between Banach spaces (operator ideals) that are defined, or characterized, by means of the transformation of vector-valued sequences. We begin by stating some known results on Functional Analysis that will be useful later. Next we study the spaces of vector-valued sequences (sequence spaces) that shall be important examples of sequences classes and that will provide examples of operator ideals of the sort we are studying. Next we present an abstract framework, called sequence classes (in the sense of Botelho and Campos [4]), which will be the background of the operators ideals we shall contruct. The next step is the introduction and the investigation of the operator ideals characterized by means of the transformation of sequence classes. Finally we show that several classical operator ideals are particular instances of the abstract framework constructed before. Special properties of these ideals are also investigated.