Moduleability, algebraic structures, and nonlinear properties
| dc.contributor.author | García-Pacheco, F.J. | |
| dc.contributor.author | Pérez-Eslava, C. | |
| dc.contributor.author | Seoane Sepúlveda, Juan Benigno | |
| dc.date.accessioned | 2023-06-20T00:26:16Z | |
| dc.date.available | 2023-06-20T00:26:16Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | We show that some pathological phenomena occur more often than one could expect, existing large algebraic structures (infinite dimensional vector spaces, algebras, positive cones or infinitely generated modules) enjoying certain special properties. In particular we construct infinite dimensional vector spaces of non-integrable, measurable functions, completing some recent results shown in Garcia-Pacheco et al. (2009) [13], Garcia-Pacheco and Seoane-Sepulveda (2006) [15], Munoz-Fernandez et al. (2008) [20]. We prove, as well, the existence of dense and not barrelled spaces of sequences every non-zero element of which has a finite number of zero coordinates (giving partial answers to a problem originally posed by R.M. Aron and V.I. Gurariy in 2003). | |
| 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.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/19988 | |
| dc.identifier.doi | 10.1016/j.jmaa.2010.05.016 | |
| dc.identifier.issn | 0022-247X | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/journal/0022247X | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42564 | |
| dc.issue.number | 1 | |
| dc.journal.title | Journal of Mathematical Analysis and Applications | |
| dc.language.iso | eng | |
| dc.page.final | 167 | |
| dc.page.initial | 159 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | MTM2009-07848. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Lineability | |
| dc.subject.keyword | Spaceability | |
| dc.subject.keyword | Algebrability | |
| dc.subject.keyword | Differentiable functions | |
| dc.subject.keyword | Measurable functions | |
| dc.subject.keyword | Integrable functions | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Moduleability, algebraic structures, and nonlinear properties | |
| dc.type | journal article | |
| dc.volume.number | 370 | |
| dcterms.references | A. Aizpuru, F.J. García-Pacheco, C. Pérez-Eslava, J.B.Seoane-Sepúlveda, Lineability and coneability of discontinuous functions on R, Publ. Math. Debrecen 72 (1–2) (2008) 129–139. R.M. Aron, J.A. Conejero, A. Peris, J.B. Seoane-Sepúlveda,Uncountably generated algebras of everywhere surjective functions, Bull. Belg. Math. Soc.Simon Stevin 17 (2010) 1–5. 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. 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. R.M. Aron, D. García, M. Maestre, Linearity in non-linear problems, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 95 (2001) 7–12. R.M. Aron, J.B. Seoane-Sepúlveda, Algebrability of the set of everywhere surjective functions on C, Bull. Belg. Math.Soc. Simon Stevin 13 (2006) 1–7. D. Azagra, G. Muñoz-Fernández, V.M. Sánchez, J.B. Seoane-Sepúlveda, Riemann integrability and Lebesgue measurability of the composite function,J. Math. Anal. Appl. 354 (2009)229–233. L. Bernal-González, Dense-lineability in spaces of continuous functions, Proc. Amer. Math. Soc. 136 (2008)3163–3169. G. Botelho, D. Diniz, D. Pellegrino, Lineability of the set of bounded linear non-absolutely summing operators, J.Math. Anal. Appl. 357 (2009) 171–175. G. Botelho, M. Matos, D. Pellegrino, Lineability of summing sets of homogeneous polynomials, Linear Multilinear Algebra 58 (1) (2010) 61–74. V. Fonf, V.I. Gurariy, V. Kadeˇc, An infinite dimensional subspace of C[0, 1] consisting of nowhere differentiable functions, C. R. Acad. Bulgare Sci. 52 (11–12) (1999) 13–16. D. García, B.C. Grecu, M. Maestre, J.B. Seoane-Sepúlveda,Infinite dimensional Banach spaces of functions with nonlinear properties, Math. Nachr. 283 (5)(2010) 712–720. F.J. García-Pacheco, M. Martín, J.B. Seoane-Sepúlveda,Lineability, spaceability, and algebrability of certain subsets of function spaces, Taiwanese J. Math.13 (4) (2009) 1257–1269. V.I. Gurariy, L. Quarta, On lineability of sets of continuous functions, J. Math. Anal. Appl. 294 (2004) 62–72. F.J. García-Pacheco, J.B. Seoane-Sepúlveda, Vector spaces of non-measurable functions, Acta Math. Sin. (Engl. Ser.)22 (6) (2006) 1805–1808. F.J. García-Pacheco, N. Palmberg, J.B. Seoane-Sepúlveda,Lineability and algebrability of pathological phenomena in analysis, J. Math. Anal. Appl. 326 (2007) 929–939. B. Gelbaum, J. Olmsted, Counterexamples in Analysis,Dover, 2003. V.I. Gurariy, Subspaces and bases in spaces of continuous functions, Dokl. Akad. Nauk SSSR 167 (1966) 971–973 (in ussian). V.I. Gurariy, Linear spaces composed of nondifferentiable functions, C. R. Acad. Bulgare Sci. 44 (5) (1991) 13–16. G. Muñoz-Fernández, N. Palmberg, D. Puglisi, J.B. Seoane-Sepúlveda, Lineability in subsets of measure and function spaces, Linear Algebra Appl.428 (11–12) (2008) 2805–2812. D. Puglisi, J.B. Seoane-Sepúlveda, Bounded linear non-absolutely summing operators, J. Math. Anal. Appl. 338 (2008) 292–298. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | e85d6b14-0191-4b04-b29b-9589f34ba898 | |
| relation.isAuthorOfPublication.latestForDiscovery | e85d6b14-0191-4b04-b29b-9589f34ba898 |
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