Sobre certas relações entre classes de operadores lineares e multilineares em espaços de Banach

• Autor(a) principal: Nascimento, Antonio Araújo do
• Data de Publicação: 2023
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/123456789/31377
• topic: Espaços de Banach; Teoria de operadores; Operadores somantes; Classes de sequências; Normas tensoriais; Banach spaces; Operator theory; Summing operators; Sequence classes; Tensor norms; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The goal of this work is to present certain relations between the linear and multilinear theories of operators in Banach spaces, establishing results based on these relations. First, we present a class of mid-summing linear operators and a somewhat convenient relationship between these operators and certain classes of multiple summing multilinear operators. As a consequence, we establish inclusions and coincidence results for the presented class of linear operators. Next, we present a result, in a certain way, in the opposite direction of the previous one, with which it is possible to characterize classes of n-linear applications through the continuity of (n − 1)-linear operators. In this case we present applications of the result to bilinear operators.