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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.07203 |
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| _version_ | 1866911368668512256 |
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| author | Kubrusly, C. S. Stankovic, H. M |
| author_facet | Kubrusly, C. S. Stankovic, H. M |
| contents | The paper extends three results regarding the nth root problem by embedding classes of Hilbert-space operators into the class of posinormal operators. For instance, it is shown that (i) for coposinormal operators, if T is paranormal and T^n is quasinormal, then T is normal, and (ii) for posinormal operators, if T is k-quasiparanormal and T^n is normal, then T is normal. Moreover, (iii) it is also shown that the latter result is not conditioned to the separability of the underlying Hilbert space, even if T is not posinormal, where, in such a case, T is the direct sum of a normal operator with a nilpotent one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07203 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Posinormality and the Root Problem Kubrusly, C. S. Stankovic, H. M Functional Analysis 47B15, 47B20 The paper extends three results regarding the nth root problem by embedding classes of Hilbert-space operators into the class of posinormal operators. For instance, it is shown that (i) for coposinormal operators, if T is paranormal and T^n is quasinormal, then T is normal, and (ii) for posinormal operators, if T is k-quasiparanormal and T^n is normal, then T is normal. Moreover, (iii) it is also shown that the latter result is not conditioned to the separability of the underlying Hilbert space, even if T is not posinormal, where, in such a case, T is the direct sum of a normal operator with a nilpotent one. |
| title | Posinormality and the Root Problem |
| topic | Functional Analysis 47B15, 47B20 |
| url | https://arxiv.org/abs/2601.07203 |