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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Refaad
2020
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| Online Access: | 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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| Institution: | Universiti Putra Malaysia |
| Language: | English |
| Summary: | 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. |
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