Operators with diskcyclic vectors subspaces
In this paper, we prove that if T is diskcyclic operator then the closed unit disk multiplied by the union of the numerical range of all iterations of T is dense in H. Also, if T is diskcyclic operator and |λ| ≤ 1, then T – λI has dense range. Moreover, we prove that if α > 1, then 1/αT is hyperc...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taibah University
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/56228/1/Operators%20with%20diskcyclic%20vectors%20subspaces.pdf |
| _version_ | 1825931374686633984 |
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| author | Bamerni, Nareen Kilicman, Adem |
| author_facet | Bamerni, Nareen Kilicman, Adem |
| author_sort | Bamerni, Nareen |
| collection | UPM |
| description | In this paper, we prove that if T is diskcyclic operator then the closed unit disk multiplied by the union of the numerical range of all iterations of T is dense in H. Also, if T is diskcyclic operator and |λ| ≤ 1, then T – λI has dense range. Moreover, we prove that if α > 1, then 1/αT is hypercyclic in a separable Hilbert space H if and only if T ⊕ αIC is diskcyclic in H ⊕ C. We show at least in some cases a diskcyclic operator has an invariant, dense linear subspace or an infinite dimensional closed linear subspace, whose non-zero elements are diskcyclic vectors. However, we give some counterexamples to show that not always a diskcyclic operator has such a subspace. |
| first_indexed | 2024-03-06T09:25:46Z |
| format | Article |
| id | upm.eprints-56228 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:25:46Z |
| publishDate | 2015 |
| publisher | Taibah University |
| record_format | dspace |
| spelling | upm.eprints-562282017-07-04T02:48:17Z http://psasir.upm.edu.my/id/eprint/56228/ Operators with diskcyclic vectors subspaces Bamerni, Nareen Kilicman, Adem In this paper, we prove that if T is diskcyclic operator then the closed unit disk multiplied by the union of the numerical range of all iterations of T is dense in H. Also, if T is diskcyclic operator and |λ| ≤ 1, then T – λI has dense range. Moreover, we prove that if α > 1, then 1/αT is hypercyclic in a separable Hilbert space H if and only if T ⊕ αIC is diskcyclic in H ⊕ C. We show at least in some cases a diskcyclic operator has an invariant, dense linear subspace or an infinite dimensional closed linear subspace, whose non-zero elements are diskcyclic vectors. However, we give some counterexamples to show that not always a diskcyclic operator has such a subspace. Taibah University 2015 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/56228/1/Operators%20with%20diskcyclic%20vectors%20subspaces.pdf Bamerni, Nareen and Kilicman, Adem (2015) Operators with diskcyclic vectors subspaces. Journal of Taibah University for Science, 9 (3). pp. 414-419. ISSN 1658-3655; ESSN: 1658-3612 http://www.sciencedirect.com/science/article/pii/S1658365515000655# 10.1016/j.jtusci.2015.02.020 |
| spellingShingle | Bamerni, Nareen Kilicman, Adem Operators with diskcyclic vectors subspaces |
| title | Operators with diskcyclic vectors subspaces |
| title_full | Operators with diskcyclic vectors subspaces |
| title_fullStr | Operators with diskcyclic vectors subspaces |
| title_full_unstemmed | Operators with diskcyclic vectors subspaces |
| title_short | Operators with diskcyclic vectors subspaces |
| title_sort | operators with diskcyclic vectors subspaces |
| url | http://psasir.upm.edu.my/id/eprint/56228/1/Operators%20with%20diskcyclic%20vectors%20subspaces.pdf |
| work_keys_str_mv | AT bamerninareen operatorswithdiskcyclicvectorssubspaces AT kilicmanadem operatorswithdiskcyclicvectorssubspaces |