The Brown Measure of Non-Hermitian Sums of Projections
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910715816706048 |
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| author | Zhou, Max Sun |
| author_facet | Zhou, Max Sun |
| contents | We compute the Brown measure of the non-normal operators $X = p + i q$, where $p$ and $q$ are Hermitian, freely independent, and have spectra consisting of $2$ atoms. The computation relies on the model of the non-trivial part of the von Neumann algebra generated by 2 projections as $2 \times 2$ random matrices. We observe that these measures are supported on hyperbolas and note some other properties related to their atoms and symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13804 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Brown Measure of Non-Hermitian Sums of Projections Zhou, Max Sun Operator Algebras Probability We compute the Brown measure of the non-normal operators $X = p + i q$, where $p$ and $q$ are Hermitian, freely independent, and have spectra consisting of $2$ atoms. The computation relies on the model of the non-trivial part of the von Neumann algebra generated by 2 projections as $2 \times 2$ random matrices. We observe that these measures are supported on hyperbolas and note some other properties related to their atoms and symmetries. |
| title | The Brown Measure of Non-Hermitian Sums of Projections |
| topic | Operator Algebras Probability |
| url | https://arxiv.org/abs/2411.13804 |