On linear chaos in function spaces
We show that, in Lp(0,∞){L}_{p}\left(0,\infty ) (1≤p<∞1\le p\lt \infty ), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C0[0,∞){C}_{0}{[}0,\infty ) and describe the spectra of the weighted translations prov...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-05-01
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| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2022-0008 |
| _version_ | 1811203667947159552 |
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| author | Jimenez John M. Markin Marat V. |
| author_facet | Jimenez John M. Markin Marat V. |
| author_sort | Jimenez John M. |
| collection | DOAJ |
| description | We show that, in Lp(0,∞){L}_{p}\left(0,\infty ) (1≤p<∞1\le p\lt \infty ), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C0[0,∞){C}_{0}{[}0,\infty ) and describe the spectra of the weighted translations provided the underlying spaces are complex. |
| first_indexed | 2024-04-12T02:59:37Z |
| format | Article |
| id | doaj.art-86a89250181c44a995e7af26a7caa1e0 |
| institution | Directory Open Access Journal |
| issn | 2391-4661 |
| language | English |
| last_indexed | 2024-04-12T02:59:37Z |
| publishDate | 2022-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj.art-86a89250181c44a995e7af26a7caa1e02022-12-22T03:50:42ZengDe GruyterDemonstratio Mathematica2391-46612022-05-0155111913510.1515/dema-2022-0008On linear chaos in function spacesJimenez John M.0Markin Marat V.1Department of Mathematics, De Anza College, 21250 Stevens Creek Blvd., Cupertino, CA 95014, USADepartment of Mathematics, California State University, Fresno, 5245 N. Backer Avenue, M/S PB 108, Fresno, CA 93740-8001, USAWe show that, in Lp(0,∞){L}_{p}\left(0,\infty ) (1≤p<∞1\le p\lt \infty ), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to C0[0,∞){C}_{0}{[}0,\infty ) and describe the spectra of the weighted translations provided the underlying spaces are complex.https://doi.org/10.1515/dema-2022-0008hypercyclic vectorperiodic pointhypercyclic operatorchaotic operatorspectrum47a1647b3747b3847a10 |
| spellingShingle | Jimenez John M. Markin Marat V. On linear chaos in function spaces Demonstratio Mathematica hypercyclic vector periodic point hypercyclic operator chaotic operator spectrum 47a16 47b37 47b38 47a10 |
| title | On linear chaos in function spaces |
| title_full | On linear chaos in function spaces |
| title_fullStr | On linear chaos in function spaces |
| title_full_unstemmed | On linear chaos in function spaces |
| title_short | On linear chaos in function spaces |
| title_sort | on linear chaos in function spaces |
| topic | hypercyclic vector periodic point hypercyclic operator chaotic operator spectrum 47a16 47b37 47b38 47a10 |
| url | https://doi.org/10.1515/dema-2022-0008 |
| work_keys_str_mv | AT jimenezjohnm onlinearchaosinfunctionspaces AT markinmaratv onlinearchaosinfunctionspaces |