Bounded and unbounded polynomials and multilinear forms: Characterizing continuity
| dc.contributor.author | Gámez Merino, José Luis | |
| dc.contributor.author | Muñoz-Fernández, Gustavo A. | |
| dc.contributor.author | Pellegrino, Daniel | |
| dc.contributor.author | Seoane Sepúlveda, Juan Benigno | |
| dc.date.accessioned | 2023-06-20T00:18:10Z | |
| dc.date.available | 2023-06-20T00:18:10Z | |
| dc.date.issued | 2012-01 | |
| dc.description.abstract | In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the question as to whether a polynomial is continuous if and only jilt transforms connected sets into connected sets. These results motivate the natural question as to how many non-continuous polynomials there are on an infinite dimensional normed space. A problem on the lineability of the sets of non-continuous polynomials and multilinear mappings on infinite dimensional normed spaces is answered. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Spanish Ministry of Science and Innovation | |
| dc.description.sponsorship | CNPq | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16877 | |
| dc.identifier.doi | 10.1016/j.laa.2011.06.050 | |
| dc.identifier.issn | 0024-3795 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0024379511005003 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42358 | |
| dc.issue.number | 1 | |
| dc.journal.title | Linear Algebra and its Applications | |
| dc.language.iso | eng | |
| dc.page.final | 242 | |
| dc.page.initial | 237 | |
| dc.publisher | Elsevier Science | |
| dc.relation.projectID | MTM2009-07848 | |
| dc.relation.projectID | 620108/2008-9 (Edital Casadinho). | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Lineability | |
| dc.subject.keyword | continuous polynomial | |
| dc.subject.keyword | non-continuous polynomial | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Bounded and unbounded polynomials and multilinear forms: Characterizing continuity | |
| dc.type | journal article | |
| dc.volume.number | 436 | |
| dcterms.references | 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) 571–575. R.M. Aron, F.J. García-Pacheco, D. Pérez-García, J.B. Seoane-Sepúlveda, On dense-lineability of sets of functions on R, Topology 48 (2009) 149–156. R.M. Aron, V.I. Gurariy, J.B. Seoane-Sepúlveda, Lineability and spaceability of sets of functions on R, Proc. Amer.Math. Soc. 133 (3) (2005) 795–803. 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, J.B. Seoane-Sepúlveda, Algebrability of the set of everywhere surjective functions on C, Bull. Belg. Math. Soc. Simon Stevin 14 (1) (2007) 25–31. L. Bernal-González, Dense-lineability in spaces of continuous functions, Proc. Amer. Math. Soc. 136 (9) (2008) 3163–3169. G. Botelho, D. Diniz, V. Fávaro, D. Pellegrino, Spaceability in Banach and quasi-Banach sequence spaces, Linear Algebra Appl. 434 (5) (2011) 1255–1260. G. Botelho, D. Diniz, D. Pellegrino, Lineability of the set of bounded linear non-absolutely summing operators, J. Math. Anal. Appl. 357 (1) (2009) 171–175. G. Botelho, M. Matos, D. Pellegrino, Lineability of summing sets of homogeneous polynomials, Linear and Multilinear Algebra 58 (1) (2010) 61–74. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1999. J.L. Gámez-Merino, G.A. Muñoz-Fernández, J.B. Seoane-Sepúlveda, A characterization of continuity revisited, Amer. Math. Monthly 118 (2) (2011) 167–170. J.L. Gámez-Merino, G.A. Muñoz-Fernández, J.B. Seoane-Sepúlveda, V. Sánchez, Sierpin´ ski–Zygmund functions and other problems on lineability, Proc. Amer. Math. Soc. 138 (2010) 3863–3876. 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. G.A. 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(1)(2008) 292–298. D.J. Velleman, Characterizing continuity, Amer. Math. Monthly 104 (1997) 318–322. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 82bc6afe-22a9-4152-a980-f481478623eb | |
| relation.isAuthorOfPublication | e85d6b14-0191-4b04-b29b-9589f34ba898 | |
| relation.isAuthorOfPublication.latestForDiscovery | 82bc6afe-22a9-4152-a980-f481478623eb |
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