Lineability criteria, with applications
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, ma...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2014 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/43011 |
| Acesso em linha: | http://hdl.handle.net/11441/43011 https://doi.org/10.1016/j.jfa.2013.11.014 |
| Access Level: | acceso abierto |
| Palavra-chave: | Lineability Maximal dense-lineability Spaceability Strict-order integrability Hypercyclicity Non-continuable holomorphic functions Fast growth entire functions Peano curves |
| Resumo: | 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. |
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