An Extension of Hypercyclicity for N-Linear Operators
Grosse-Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. We propose an alternative notion of orbit for N-linear operators that is inspired by difference equations. Under this new notion, every separable infinite di...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/609873 |
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| author | Juan Bès J. Alberto Conejero |
| author_facet | Juan Bès J. Alberto Conejero |
| author_sort | Juan Bès |
| collection | DOAJ |
| description | Grosse-Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. We propose an alternative notion of orbit for N-linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic N-linear operators, for each N≥2. Indeed, the nonnormable spaces of entire functions and the countable product of lines support N-linear operators with residual sets of hypercyclic vectors, for N=2. |
| format | Article |
| id | doaj-art-a75cf68662d0482e841deb5234240562 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a75cf68662d0482e841deb52342405622025-02-03T05:54:30ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/609873609873An Extension of Hypercyclicity for N-Linear OperatorsJuan Bès0J. Alberto Conejero1Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USAInstituto Universitario de Matemática Pura y Aplicada, Universitat Politécnica de Valéncia, 46022 Valéncia, SpainGrosse-Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. We propose an alternative notion of orbit for N-linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic N-linear operators, for each N≥2. Indeed, the nonnormable spaces of entire functions and the countable product of lines support N-linear operators with residual sets of hypercyclic vectors, for N=2.http://dx.doi.org/10.1155/2014/609873 |
| spellingShingle | Juan Bès J. Alberto Conejero An Extension of Hypercyclicity for N-Linear Operators Abstract and Applied Analysis |
| title | An Extension of Hypercyclicity for N-Linear Operators |
| title_full | An Extension of Hypercyclicity for N-Linear Operators |
| title_fullStr | An Extension of Hypercyclicity for N-Linear Operators |
| title_full_unstemmed | An Extension of Hypercyclicity for N-Linear Operators |
| title_short | An Extension of Hypercyclicity for N-Linear Operators |
| title_sort | extension of hypercyclicity for n linear operators |
| url | http://dx.doi.org/10.1155/2014/609873 |
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