Counterexamples related to unbounded paranormal operators
In this paper, we give an example of a densely defined non-closable paranormal operator. Then, we give another example of a densely defined closable paranormal operator whose closure fails to be paranormal. It is worth noticing that our first example says that the adjoint of a densely defined parano...
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| Format: | Article |
| Language: | English |
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Elsevier
2021-11-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X21000100 |
| Summary: | In this paper, we give an example of a densely defined non-closable paranormal operator. Then, we give another example of a densely defined closable paranormal operator whose closure fails to be paranormal. It is worth noticing that our first example says that the adjoint of a densely defined paranormal operator may have a trivial domain. In the end, we give an example of a densely defined closed one-to-one paranormal operator T whose adjoint is also injective and paranormal, but T is not normal. |
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| ISSN: | 2666-657X |