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Operators with diskcyclic vectors subspaces


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


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
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