Espaços quase-banach e resultados estruturantes

• Ano de defesa: 2023
• Autor(a) principal: Demétrio Júnior, Evandio
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Matemática; Espaços vetoriais topológicos; Espaços localmente convexos; Aoki-Rolewicz; F-norma; Banach-Grunblum-Nikolskii; Topological vector spaces; Locally convex spaces; Quasi-norm; F-norm; HBEP; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/30470

This text studies fundamental concepts and structures in topological vector spaces, focusing on locally convex and quasi-normed spaces. The latter has a structure similar to normed spaces but generally is not a locally convex environment. Throughout the text, we explore the relevant aspects of the investigated environments and highlight their importance through structuring results. We investigate F-spaces from various perspectives and present classical results from the theory of Banach spaces in this context. Overview notions of the concepts of bases in topological vector spaces are studied, particularly the relationship between the extension of linear functionals and local convexity, usually known as the Hahn-Banach Extension Property (HBEP).