A propriedade positiva de Schur em reticulados de Banach

• Autor(a) principal: Tabares, Juan David Rubio
• Data de Publicação: 2024
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFU
• Texto Completo: https://repositorio.ufu.br/handle/123456789/43171; http://doi.org/10.14393/ufu.di.2024.174
• topic: Reticulados de Banach; Propriedade de Schur Positiva; Espaço de operadores regulares; Convergência fraca; Operadores compactos; Operadores fracamente compactos; Banach lattices; positive Schur property; regular operators; compact operators; weakly compact operators; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE::ANALISE FUNCIONAL; Matemática; Banach, Álgebra de; Operadores diferenciais parciais; Teorema; ODS::ODS 17. Parcerias e meios de implementação - Fortalecer os meios de implementação e revitalizar a parceria global para o desenvolvimento sustentável.

The purpose of this dissertation is to study, in several aspects, the positive Schur property in Banach lattices. In order to justify the example of a Banach lattice with the positive Schur property failing the Schur property, a criterion for weak convergence in L 1 [0, 1], which recovers the Rademacher sequence as a particular instance, is proved. Examples, counterexamples and several properties of the positive Schur property are provided. We also study this property in countable direct sums and in l p (Γ)-spaces. Next, the positive Schur property in spaces of regular operators is investigated, and a lattice version of Ryan’s Theorem is proved. Finally, several characterizations of the positive Schur property in dual lattices are proved.