On dense-lineability of sets of functions on R
| dc.contributor.author | Aron, R.M. | |
| dc.contributor.author | García-Pacheco, F.J. | |
| dc.contributor.author | Pérez García, David | |
| dc.contributor.author | Seoane Sepúlveda, Juan Benigno | |
| dc.date.accessioned | 2023-06-20T00:22:59Z | |
| dc.date.available | 2023-06-20T00:22:59Z | |
| dc.date.issued | 2009 | |
| dc.description.abstract | A subset M of a topological vector space X is said to be dense-lineable in X if there exists an infinite dimensional linear manifold in M boolean OR {0} and dense in X. We give sufficient conditions for a lineable set to be dense-lineable, and we apply them to prove the dense-lineability of several subsets of e[a, b]. We also develop some techniques to show that the set of differentiable nowhere monotone functions is dense-lineable in e[a, b]. Other results related to density and dense-lineability of sets in Banach spaces are also presented. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación | |
| dc.description.sponsorship | Ministerio de Educación y Ciencia | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17714 | |
| dc.identifier.doi | 10.1016/j.top.2009.11.013 | |
| dc.identifier.issn | 0040-9383 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0040938309000251 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42487 | |
| dc.issue.number | 2-4 | |
| dc.journal.title | Topology | |
| dc.language.iso | eng | |
| dc.page.final | 156 | |
| dc.page.initial | 149 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | (MTM2008-03211) | |
| dc.relation.projectID | (MTM2006-15546) | |
| dc.relation.projectID | (MTM2005-00082) | |
| dc.relation.projectID | Grant( MTM2006-03531) | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.53 | |
| dc.subject.keyword | Dense-lineability | |
| dc.subject.keyword | differentiable nowhere monotone functions | |
| dc.subject.ucm | Funciones (Matemáticas) | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | On dense-lineability of sets of functions on R | |
| dc.type | journal article | |
| dc.volume.number | 48 | |
| dcterms.references | R.M. Aron, V.I. Gurariy, J.B. Seoane-Sepúlveda, Lineability and spaceability of sets of functions on R, Proc. Amer. Math. Soc. 133 (2005) 795-803. V.I. Gurariy, L. Quarta, On lineability of sets of continuous functions, J. Math. Anal. Appl. 294 (2004) 62-72. R.M. Aron, D. García, M. Maestre, Linearity in non-linear problems, RACSAM Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 95 (1) (2001) 7-12. F. Bayart, Topological and algebraic genericity of divergence and universality, Studia Math. 167 (2005) 161-181. R.M. Aron, D. Pérez-García, J.B. Seoane-Sepúlveda, Algebrability of the set of non-convergent Fourier series, Studia Math. 175 (1) (2006) 83-90. A.B. Kharazishvili, Strange functions in real analysis, in: CRC Pure and Appl. Math., Chapman & Hall, 2006. F. Bayart, L. Quarta, Algebras in sets of queer functions, Israel J. Math. 158 (2007) 285-296. L. Bernal-González, Dense-lineability in spaces of continuous functions, Proc. Amer. Math. Soc. 136 (2008) 3163-3169. V.I. Gurariy, Linear spaces composed of everywhere nondifferentiable functions, C.R. Acad. Bulgare Sci. 44 (5) (1991) 13-16. (in Russian). F.J. García-Pacheco, N. Palmberg, J.B. Seoane-Sepúlveda, Lineability and algebrability of pathological phenomena in analysis, J. Math. Anal. Appl. 326 (2) (2007) 929-939. L. Bernal-González, Lineability of sets of nowhere analytic functions, J. Math. Anal. Appl. 340 (2008) 1284-1295. G.R. MacLane, Sequences of derivatives and normal families, J. Anal. Math. 2 (1952) 72-87. G. Godefroy, J.H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal. 98 (1991) 229-269. J. Wengenroth, Hypercyclic operators on non-locally convex spaces, Proc. Amer. Math. Soc. 131 (2003) 1759-1761. G.A. Muñoz-Fernández, N. Palmberg, D. Puglisi, J.B. Seoane-Sepúlveda, Lineability in subsets of measure and function spaces, Linear Algebra Appl. 428(2008) 2805-2812. | |
| dspace.entity.type | Publication | |
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| relation.isAuthorOfPublication | e85d6b14-0191-4b04-b29b-9589f34ba898 | |
| relation.isAuthorOfPublication.latestForDiscovery | 5edb2da8-669b-42d1-867d-8fe3144eb216 |
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