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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taibah University
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/56228/1/Operators%20with%20diskcyclic%20vectors%20subspaces.pdf http://psasir.upm.edu.my/id/eprint/56228/ http://www.sciencedirect.com/science/article/pii/S1658365515000655# |
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| Institution: | Universiti Putra Malaysia |
| Language: | English |
| Summary: | 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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