Positive self-commutators of positive operators
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916554856202240 |
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| author | Drnovšek, Roman Kandić, Marko |
| author_facet | Drnovšek, Roman Kandić, Marko |
| contents | We consider a positive operator $A$ on a Hilbert lattice such that its self-commutator $C = A^* A - A A^*$ is positive. If $A$ is also idempotent, then it is an orthogonal projection, and so $C = 0$. Similarly, if $A$ is power compact, then $C = 0$ as well. We prove that every positive compact central operator on a separable infinite-dimensional Hilbert lattice $\mathcal H$ is a self-commutator of a positive operator. We also show that every positive central operator on $\mathcal H$ is a sum of two positive self-commutators of positive operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positive self-commutators of positive operators Drnovšek, Roman Kandić, Marko Functional Analysis 46B42, 47B65, 47B47 We consider a positive operator $A$ on a Hilbert lattice such that its self-commutator $C = A^* A - A A^*$ is positive. If $A$ is also idempotent, then it is an orthogonal projection, and so $C = 0$. Similarly, if $A$ is power compact, then $C = 0$ as well. We prove that every positive compact central operator on a separable infinite-dimensional Hilbert lattice $\mathcal H$ is a self-commutator of a positive operator. We also show that every positive central operator on $\mathcal H$ is a sum of two positive self-commutators of positive operators. |
| title | Positive self-commutators of positive operators |
| topic | Functional Analysis 46B42, 47B65, 47B47 |
| url | https://arxiv.org/abs/2501.03733 |