Unimodular multilinear forms on sequence spaces and summability principles

• Ano de defesa: 2020
• Autor(a) principal: Santos, Lisiane Rezende dos
• Tipo de documento: Tese
• 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: Desigualdade de Kahane–Salem–Zygmund; Formas unimodulares; Estimativas assintóticas; Operadores somantes; Teorema de inclusão; Princípio de regularidade; Desigualdade de Hardy–Littlewood; Kahane–Salem–Zygmund inequality; Asymptotic estimates; Unimodular forms; Summing operators; Inclusion theorems; Regularity principle; Hardy–Littlewood inequality; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/26204

This work is divided into two parts. Initially, we investigate the existence of unimodular (complex or real) forms with relatively small norms on (Fórmula) spaces. We improve the sup norm upper estimate in Kahane–Salem–Zygmund inequality for multilinear forms: given positive (Fórmula) there exists an m-linear map (Fórmula) where (Fórmula) is a constant. This norm estimate is used to offer a definitive answer to the asymptotic behavior from infimum of norms of unimodular forms on (Fórmula). The second part concerns the summability of operators and related subjects. We apply a recent technique introduced by Pellegrino et al. [56] to obtain an improved regularity principle on sequence spaces and an inclusion theorem for summing operators. Next, we deal with a general summability notion (Λ–summing operators, see Chapter 3) that unifies the multiple and absolutely summing operators. A general inclusion theorem that encompasses the correspondent result on each class is provided. We also obtain applications to the multilinear Hardy–Littlewood inequality in both contexts.