Opened Access Lineability criteria, with applications


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Autor: Bernal González, Luis
Ordóñez Cabrera, Manuel Hilario
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2014-03-15
Publicado en: Journal of Functional Analysis, 266 (6), 3997-4025.
Tipo de documento: Artículo
Resumen: Lineability is a property enjoyed by some subsets within a vector space X. A subset A of X is called lineable whenever A contains, except for zero, an infinite dimensional vector subspace. If, additionally, X is endowed with richer structures, then the more stringent notions of dense-lineability, maximal dense-lineability and spaceability arise naturally. In this paper, several lineability criteria are provided and applied to specific topological vector spaces, mainly function spaces. Sometimes, such criteria furnish unified proofs of a number of scattered results in the related literature. Families of strict-order integrable functions, hypercyclic vectors, non-extendable holomorphic mappings, Riemann non-Lebesgue integrable functions, sequences not satisfying the Lebesgue dominated convergence theorem, nowhere analytic functions, bounded variation functions, entire functions with fast growth and Peano curves, among others, are analyzed from the point of view of lineability.
Cita: Bernal González, L. y Ordóñez Cabrera, M.H. (2014). Lineability criteria, with applications. Journal of Functional Analysis, 266 (6), 3997-4025.
Tamaño: 391.8Kb
Formato: PDF


DOI: 10.1016/j.jfa.2013.11.014

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