Lineability, spaceability, and algebrability of certain subsets of function spaces.
| dc.contributor.author | García-Pacheco, F.J. | |
| dc.contributor.author | Martín Conde, María | |
| dc.contributor.author | Seoane Sepúlveda, Juan Benigno | |
| dc.date.accessioned | 2023-06-20T10:33:06Z | |
| dc.date.available | 2023-06-20T10:33:06Z | |
| dc.date.issued | 2009 | |
| dc.description.abstract | We construct infinite-dimensional Banach spaces and infinitely generated Banach algebras of functions that, except for 0, satisfy some kind of special or pathological property. Three of these structures are: a Banach algebra of everywhere continuous bounded functions which are not Riemann-integrable; a Banach space of Lebesgue-integrable functions that are not Riemann-integrable; an algebra of continuous unbounded functions defined on an arbitrary non-compact metric space. | |
| 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 | MEC | |
| dc.description.sponsorship | MEC | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20032 | |
| dc.identifier.issn | 1027-5487 | |
| dc.identifier.officialurl | http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/463/349 | |
| dc.identifier.relatedurl | http://tjm.math.ntu.edu.tw/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50457 | |
| dc.issue.number | 4 | |
| dc.journal.title | Taiwanese Journal of Mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 1269 | |
| dc.page.initial | 1257 | |
| dc.publisher | Mathematical Soc Rep China | |
| dc.relation.projectID | MTM 2006-04837. | |
| dc.relation.projectID | MTM 2006-03531 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Riemann integrable | |
| dc.subject.keyword | Lebesgue integrable | |
| dc.subject.keyword | Continuous unbounded functions | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Lineability, spaceability, and algebrability of certain subsets of function spaces. | |
| dc.type | journal article | |
| dc.volume.number | 13 | |
| dcterms.references | R. M. Aron, D. Garcia and M. Maestre, Linearity in non-linear problems, RACSAM Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat., 95(1) (2001), 7-12. R. M. Aron, V. I. Gurariy and J. B. Seoane-Sepulveda,Lineability and spaceability of sets of functions on R, Proc. Amer. Math. Soc., 133 (2005), 795-803. R. M. Aron, D. Perez-Garcla and J. B. Seoane-Sepulveda,Algebrability of the set of non-convergent Fourier series, Studia Math., 175(1) (2006), 83-90. R. M. Aron and J. B. Seoane-Sepulveda, Algebrability of the set of everywhere surjective functions on C, Bull. Belg.Math. Soc. Simon Stevin, 14(1) (2007),25-31. F. Bayart and L. Quarta, Algebras in sets of queer functions, Isr. J. Math., 158 (2007), 285-296. P. Enflo and V. I. Gurariy, On lineability and spaceability of sets in function spaces,Preprint. V. P. Fonf, V. I. Gurariy and M. I. Kadec, 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. Garcia, B. C. Grecu, M. Maestre, J. B. Seoane-Sepulveda. Infinite dimensional Banach spaces of functions with nonlinear properties. Preprint. F. J. Garcia-Pacheco, N. Palmberg and J. B. Seoane-Sepulveda, Lineability and algebrability of pathological phenomena in analysis, J. Math. Anal. Appl., 326 (2007),929-939. B. Gelbaum and J. Olmsted, Counterexamples in analysis,Dover, 2003. V. I. Gurariy, Subspaces and bases in spaces of continuous functions (Russian), Dokl.Akad. Nauk SSSR, 167 (1966), 971-973. V. I. Gurariy, Linear spaces composed of nondifferentiable functions, C. R. Acad.Bulgare Sci., 44(5) (1991), 13-16. V. I. Gurariy and L. Quarta, On lineability of sets of continuous functions, J. Math.Anal. Appl., 294 (2004), 62-72. S. Hencl, Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Holder functions, Proc. Amer. Math.Soc., 128(12) (2000), 3505-3511. J. Lindenstrauss, On subspaces of Banach spaces without quasi-complements, Israel J. Math., 6 (1968), 36-38. J. R. Munkres, Topology (second edition), Prentice Hall,Upper Saddle River, NJ,2000. H. P. Rosenthal, On quasi-complemented subspaces of Banach spaces, Proc. Nat.Acad. Sci. U.S.A., 59 (1968), 361-364. H. P. Rosenthal, On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from Lp(μ) to Lr(ν), J. Funct. Analysis, 4 (1969), 176-214. W. Rudin, Principles of mathematical analysis, Third edition, McGraw-Hill Book Co., New York, 1976. | |
| dspace.entity.type | Publication | |
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| relation.isAuthorOfPublication | e85d6b14-0191-4b04-b29b-9589f34ba898 | |
| relation.isAuthorOfPublication.latestForDiscovery | b4d8ca11-a569-40ec-bd29-90eba44f8f01 |
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