Espaços com propriedades especiais, lineabilidade e espaçabilidade - Sousa, Luiz Felipe de Pinho (2021)
In this work we study the theory of lineability and spaceability in the context of sequence spaces. As a background, we study the necessary basic theory, with special attention to the involved sequence spaces. We present the concept of invariant sequence spaces over some Banach space X, which abstracts several well known sequence spaces. With this concept and the appropriate techniques, we present lineability and spaceability results in sets, when these are not empty, formed by sequences with special properties. Also in this environment, we present spaceability results involving some functions and sequences of functions with special properties that, under certain restrictions, imply maximal spaceability of the studied sets.