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arXiv · 2603.19528

The spectra of polynomials in free (semi)circular operators

Akihiro Miyagawa
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Abstract

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.

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Akihiro Miyagawa. 2026-03-19. The spectra of polynomials in free (semi)circular operators. https://arxiv.org/abs/2603.19528

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