A family of matrix flows converging to normal matrices
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915794390089728 |
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| author | Izumi, Masaki |
| author_facet | Izumi, Masaki |
| contents | The celebrated Antezana-Pujals-Stojanoff Theorem states that the iterated Aluthge transforms of an arbitrary matrix converge to a normal matrix. We introduce a family of matrix flows that share this convergence property by defining them through ordinary differential equations. The family includes a continuous analogue of the Aluthge transform, as well as a differential equation discussed by Haagerup in the context of II$_1$ factors. We also examine the same type of flows in the setting of Hilbert space operators equipped with unitarily invariant norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11837 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A family of matrix flows converging to normal matrices Izumi, Masaki Functional Analysis Dynamical Systems Operator Algebras Spectral Theory The celebrated Antezana-Pujals-Stojanoff Theorem states that the iterated Aluthge transforms of an arbitrary matrix converge to a normal matrix. We introduce a family of matrix flows that share this convergence property by defining them through ordinary differential equations. The family includes a continuous analogue of the Aluthge transform, as well as a differential equation discussed by Haagerup in the context of II$_1$ factors. We also examine the same type of flows in the setting of Hilbert space operators equipped with unitarily invariant norms. |
| title | A family of matrix flows converging to normal matrices |
| topic | Functional Analysis Dynamical Systems Operator Algebras Spectral Theory |
| url | https://arxiv.org/abs/2602.11837 |