On the direct sum of two bounded linear operators and subspace-hypercyclicity
In this paper, we study the relation between subspace-hypercyclicity and the direct sum of two operators. In particular, we show that if the direct sum of two operators is subspace-hypercyclic, then both operators are subspace-hypercyclic; however, the converse is true for a stronger property than s...
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2020
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my.upm.eprints.869752022-09-05T03:51:41Z http://psasir.upm.edu.my/id/eprint/86975/ On the direct sum of two bounded linear operators and subspace-hypercyclicity Bamerni, Nareen Kilicman, Adem In this paper, we study the relation between subspace-hypercyclicity and the direct sum of two operators. In particular, we show that if the direct sum of two operators is subspace-hypercyclic, then both operators are subspace-hypercyclic; however, the converse is true for a stronger property than subspace-hypercyclicity. Moreover, we prove that if an operator T satisfies subspace-hypercyclic criterion, then T ⊕ T is subspace-hypercyclic. However, we show that the converse is true under certain conditions. Refaad 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/86975/1/On%20the%20direct%20sum%20of%20two%20bounded.pdf Bamerni, Nareen and Kilicman, Adem (2020) On the direct sum of two bounded linear operators and subspace-hypercyclicity. General Letters in Mathematics, 8 (1). pp. 1-7. ISSN 2519-9269; ESSN: 2519-9277 http://www.refaad.com/views/GLM/home.aspx |
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In this paper, we study the relation between subspace-hypercyclicity and the direct sum of two operators. In particular, we show that if the direct sum of two operators is subspace-hypercyclic, then both operators are subspace-hypercyclic; however, the converse is true for a stronger property than subspace-hypercyclicity. Moreover, we prove that if an operator T satisfies subspace-hypercyclic criterion, then T ⊕ T is subspace-hypercyclic. However, we show that the converse is true under certain conditions. |
| format |
Article |
| author |
Bamerni, Nareen Kilicman, Adem |
| spellingShingle |
Bamerni, Nareen Kilicman, Adem On the direct sum of two bounded linear operators and subspace-hypercyclicity |
| author_facet |
Bamerni, Nareen Kilicman, Adem |
| author_sort |
Bamerni, Nareen |
| title |
On the direct sum of two bounded linear operators and subspace-hypercyclicity |
| title_short |
On the direct sum of two bounded linear operators and subspace-hypercyclicity |
| title_full |
On the direct sum of two bounded linear operators and subspace-hypercyclicity |
| title_fullStr |
On the direct sum of two bounded linear operators and subspace-hypercyclicity |
| title_full_unstemmed |
On the direct sum of two bounded linear operators and subspace-hypercyclicity |
| title_sort |
on the direct sum of two bounded linear operators and subspace-hypercyclicity |
| publisher |
Refaad |
| publishDate |
2020 |
| url |
http://psasir.upm.edu.my/id/eprint/86975/1/On%20the%20direct%20sum%20of%20two%20bounded.pdf http://psasir.upm.edu.my/id/eprint/86975/ http://www.refaad.com/views/GLM/home.aspx |
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