The spectra of polynomials in free (semi)circular operators
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911610391494656 |
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| author | Miyagawa, Akihiro |
| author_facet | Miyagawa, Akihiro |
| contents | We show that any $L^2$-bounded rational function in free semicircular random variables is a bounded operator, which implies the coincidence of the usual spectrum and $L^2$-spectrum for rational functions. Based on this observation, we also compute the spectra of several polynomials in free circular random variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19528 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The spectra of polynomials in free (semi)circular operators Miyagawa, Akihiro Operator Algebras Functional Analysis Probability We show that any $L^2$-bounded rational function in free semicircular random variables is a bounded operator, which implies the coincidence of the usual spectrum and $L^2$-spectrum for rational functions. Based on this observation, we also compute the spectra of several polynomials in free circular random variables. |
| title | The spectra of polynomials in free (semi)circular operators |
| topic | Operator Algebras Functional Analysis Probability |
| url | https://arxiv.org/abs/2603.19528 |