G- Cyclicity And Somewhere Dense Orbit
let H be an infinite – dimensional separable complex Hilbert space, and S be a multiplication semigroup of with 1. An operator T is called G-cyclic over S if there is a non-zero vector xÎ H such that {aTn x½aÎS, n ≥0} is norm-dense in H. Bourdon and Feldman have proved that the existence of somew...
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| Format: | Article |
| Language: | English |
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University of Baghdad, College of Science for Women
2010-06-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/11927 |
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| author | Zeana Zaki Jamil |
| author_facet | Zeana Zaki Jamil |
| author_sort | Zeana Zaki Jamil |
| collection | DOAJ |
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let H be an infinite – dimensional separable complex Hilbert space, and S be a multiplication semigroup of with 1. An operator T is called G-cyclic over S if there is a non-zero vector xÎ H such that {aTn x½aÎS, n ≥0} is norm-dense in H. Bourdon and Feldman have proved that the existence of somewhere dense orbits implies hypercyclicity. We show the corresponding result for G-cyclicity.
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| format | Article |
| id | doaj-art-5f3cc01be0cf4363a4d6b755bd77cee8 |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2010-06-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-5f3cc01be0cf4363a4d6b755bd77cee82025-08-20T03:56:17ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862010-06-017210.21123/bsj.2010.11927G- Cyclicity And Somewhere Dense OrbitZeana Zaki Jamil let H be an infinite – dimensional separable complex Hilbert space, and S be a multiplication semigroup of with 1. An operator T is called G-cyclic over S if there is a non-zero vector xÎ H such that {aTn x½aÎS, n ≥0} is norm-dense in H. Bourdon and Feldman have proved that the existence of somewhere dense orbits implies hypercyclicity. We show the corresponding result for G-cyclicity. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/11927Hypercyclic operators, hypercyclic vectors, semigroup, somewhere dense set, everywhere dense set |
| spellingShingle | Zeana Zaki Jamil G- Cyclicity And Somewhere Dense Orbit مجلة بغداد للعلوم Hypercyclic operators, hypercyclic vectors, semigroup, somewhere dense set, everywhere dense set |
| title | G- Cyclicity And Somewhere Dense Orbit |
| title_full | G- Cyclicity And Somewhere Dense Orbit |
| title_fullStr | G- Cyclicity And Somewhere Dense Orbit |
| title_full_unstemmed | G- Cyclicity And Somewhere Dense Orbit |
| title_short | G- Cyclicity And Somewhere Dense Orbit |
| title_sort | g cyclicity and somewhere dense orbit |
| topic | Hypercyclic operators, hypercyclic vectors, semigroup, somewhere dense set, everywhere dense set |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/11927 |
| work_keys_str_mv | AT zeanazakijamil gcyclicityandsomewheredenseorbit |