Citation
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
Abstract
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.
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science |
| DOI Number: | https://doi.org/10.1016/j.jtusci.2015.02.020 |
| Publisher: | Taibah University |
| Keywords: | Diskcyclic operator; Diskcyclic vector; Diskcyclicity criterion; Condition B1; Numerical range |
| Depositing User: | Nabilah Mustapa |
| Date Deposited: | 04 Jul 2017 02:48 |
| Last Modified: | 04 Jul 2017 02:48 |
| Altmetrics: | http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1016/j.jtusci.2015.02.020 |
| URI: | http://psasir.upm.edu.my/id/eprint/56228 |
| Statistic Details: | View Download Statistic |
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