Orbits of Cesaro type operators
| dc.contributor.author | León Saavedra, F. | |
| dc.contributor.author | Piqueras Lerena, A. | |
| 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 | A bounded linear operator T on a Banach space X is called hypercyclic if there exists a vector x is an element of X such that its orbit, {T(n)x}, is dense in X. In this paper we show hypercyclic properties of the orbits of the Cesaro operator defined on different spaces. For instance, we show that the Cesaro operator defined on L(p)[0, 1] (1 < p < infinity) is hypercyclic. Moreover, it is chaotic and it has supercyclic subspaces. On the other hand, the Cesaro operator defined on other spaces of functions behave differently. Motivated by this, we study weighted Cesaro operators and different degrees of hypercyclicity are obtained. The proofs are based on the classical Muntz-Szasz theorem. We also propose problems and give new directions. | |
| 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 | Junta de Andalucia | |
| dc.description.sponsorship | UCA | |
| dc.description.sponsorship | Junta de Andalucıa | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20033 | |
| dc.identifier.doi | 10.1002/mana.200610769 | |
| dc.identifier.issn | 0025-584X | |
| dc.identifier.officialurl | http://onlinelibrary.wiley.com/doi/10.1002/mana.200610769/pdf | |
| dc.identifier.relatedurl | http://www.wiley.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50458 | |
| dc.issue.number | 5 | |
| dc.journal.title | Mathematische Nachrichten | |
| dc.language.iso | eng | |
| dc.page.final | 773 | |
| dc.page.initial | 764 | |
| dc.publisher | Wiley-Blackwell | |
| dc.relation.projectID | MTM 2006-09060 | |
| dc.relation.projectID | FQM-257 | |
| dc.relation.projectID | MTM 2006-15546-C02-01 | |
| dc.relation.projectID | FQM-257 | |
| dc.relation.projectID | MTM 2006-03531. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Hypercyclicity | |
| dc.subject.keyword | supercyclicity | |
| dc.subject.keyword | Cesaro operators | |
| dc.subject.keyword | Hypercyclic subspaces | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Orbits of Cesaro type operators | |
| dc.type | journal article | |
| dc.volume.number | 282 | |
| dcterms.references | R. M. Aron, J. B. Seoane–Sepulveda, and A. Weber, Chaos on function spaces, Bull. Aust. Math. Soc. 71, No. 3,411–415 (2005). P. S. Bourdon, Orbits of hyponormal operators, Michigan Math. J. 44, No. 2, 345–353 (1997). A. Brown, P. R. Halmos, and A. L. Shields, Cesaro operators, Acta Sci. Math. (Szeged) 26, 125–137 (1965). G. Costakis and D. Hadjiloucas, Somewhere dense Cesaro orbits and rotations of Cesaro hypercyclic operators,Studia Math. 175, No. 3, 249–269 (2006). M. De la Rosa and C. Read, A hypercyclic operator whose direct sum T ⊕ T is not hypercyclic, J. Oper. Theory, to appear. R. deLaubenfels, H. Emamirad, and K.-G. Grosse–Erdmann,Chaos for semigroups of unbounded operators, Math.Nachr. 261/262, 47–59 (2003). T. Erdelyi and W. B. Johnson, The “full Muntz theorem” in Lp[0, 1] for 0 < p < 1, J. Anal. Math. 84, 145–172 (2001). P. Gavrut¸a, Weighted Ces`aro operators, An. Univ.Timis¸oara Ser. S¸ tiint¸. Mat. 27, No. 2, 39–44 (1989). G. Godefroy and J. H. Shapiro, Operators with dense,invariant, cyclic vector manifolds, J. Funct. Anal.98, No. 2,229–269 (1991). M. Gonzalez, The fine spectrum of the Cesaro operator in lp (1 < p < 1), Arch. Math. (Basel) 44, No. 4, 355–358 (1985). M. Gonzalez, F. Leon–Saavedra, and A. Montes–Rodrıguez,Semi-Fredholm theory: hypercyclic and supercyclic subspaces,Proc. London Math. Soc. (3) 81, No. 1, 169–189 (2000). K.-G. Grosse–Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N. S.) 36, No. 3, 345–381 (1999). P. R. Halmos and V. Sunder, Bounded Integral Operators on L2 Spaces (Springer-Verlag, 1978). T. L. Kriete, III and D. Trutt, The Ces`aro operator in l2 is subnormal, Amer. J. Math. 93, 215–225 (1971). F. Leon–Saavedra, Operators with hypercyclic Cesaro means Studia Math. 152, No. 3, 201–215 (2002). F. Leon–Saavedra and V. Muller, Rotations of hypercyclic and supercyclic operators, Integral Equations Oper. Theory 50, No. 3, 385–391 (2004). F. Leon–Saavedra and V. Muller, Hypercyclic sequences of operators, Studia Math. 175, No. 1, 1–18(2006). F. Leon–Saavedra and A. Piqueras–Lerena, On weak positive supercyclicity, Israel J. Math. 167, 303–313 (2008). F. Leon–Saavedra and A. Piqueras–Lerena, Positivity in the Theory of Supercyclic Operators, Banach Center Publications Vol. 75(Polish Acad. Sci., Warsaw, 2007). T. L. Miller and V. G. Miller, Local spectral theory and orbits of operators, Proc. Amer. Math. Soc. 127, No. 4,1029–1037 (1999). T. L. Miller, V. G. Miller, and R. C. Smith, Bishop’s property (β) and the Cesaro operator, J. London Math. Soc.(2) 58,No.1, 197–207(1998). A. Montes–Rodrıguez and H. N. Salas, Supercyclic subspaces,Bull. London Math. Soc. 35, No. 6, 721–737 (2003). A. Montes–Rodr´ıguez, J. Sanchez–A´ lvarez, and J.Zemanek, Uniform Abel–Kreiss boundedness and the extremal behaviour of the Volterra operator, Proc. London Math. Soc. (3) 91,No. 3, 761–788 (2005). A. Montes–Rodrıguez and S. Shkarin, The Volterra operator is not weakly supercyclic, J. Oper. Theory, to appear. A. Montes–Rodrıguez and Stanislav A. Shkarin, New results on a classical operator, in: Recent Advances in Operator Related Function Theory, Contemporary Mathematics Vol. 393 (Amer. Math. Soc., Providence, RI, 2006), pp. 139–157. J. H. Shapiro, Composition Operators and Classical Function Theory, Universitext: Tracts in Mathematics (Springer-Verlag, New York, 1993). S. Shkarin, Antisupercyclic operators and orbits of the Volterra operator, J. London Math. Soc. (2) 73, No. 2, 506–528 (2006). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | e85d6b14-0191-4b04-b29b-9589f34ba898 | |
| relation.isAuthorOfPublication.latestForDiscovery | e85d6b14-0191-4b04-b29b-9589f34ba898 |
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