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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Refaad
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/86975/ http://psasir.upm.edu.my/id/eprint/86975/1/On%20the%20direct%20sum%20of%20two%20bounded.pdf |
| _version_ | 1848860334437171200 |
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| author | Bamerni, Nareen Kilicman, Adem |
| author_facet | Bamerni, Nareen Kilicman, Adem |
| author_sort | Bamerni, Nareen |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T12:43:35Z |
| format | Article |
| id | upm-86975 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:43:35Z |
| publishDate | 2020 |
| publisher | Refaad |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| spellingShingle | Bamerni, Nareen Kilicman, Adem On the direct sum of two bounded linear operators and subspace-hypercyclicity |
| title | 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_short | 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 |
| url | http://psasir.upm.edu.my/id/eprint/86975/ http://psasir.upm.edu.my/id/eprint/86975/ http://psasir.upm.edu.my/id/eprint/86975/1/On%20the%20direct%20sum%20of%20two%20bounded.pdf |