Positive commutators of positive square-zero operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917173344075776 |
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| author | Drnovšek, Roman Kandić, Marko |
| author_facet | Drnovšek, Roman Kandić, Marko |
| contents | In this paper we first consider the question which nonnegative matrices are commutators of nonnegative square-zero matrices. Then, we treat infinite-dimensional analogues of these results for operators on the Banach lattices $L^p[0,1]$ and $\ell^p$ ($ 1 \leq p < \infty$). In the last setting we need to extend the notion of the nonnegative rank of a nonnegative matrix. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Positive commutators of positive square-zero operators Drnovšek, Roman Kandić, Marko Functional Analysis 46B42, 47B65, 15B48, 47B47 In this paper we first consider the question which nonnegative matrices are commutators of nonnegative square-zero matrices. Then, we treat infinite-dimensional analogues of these results for operators on the Banach lattices $L^p[0,1]$ and $\ell^p$ ($ 1 \leq p < \infty$). In the last setting we need to extend the notion of the nonnegative rank of a nonnegative matrix. |
| title | Positive commutators of positive square-zero operators |
| topic | Functional Analysis 46B42, 47B65, 15B48, 47B47 |
| url | https://arxiv.org/abs/2512.22988 |