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A remark on orbital free entropy

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Abstract

A lower estimate of the orbital free entropy \(\chi _\mathrm {orb}\) under unitary conjugation is proved, and it together with Voiculescu’s observation shows that the conjectural exact formula relating \(\chi _\mathrm {orb}\) to the free entropy \(\chi \) breaks in general in contrast to the case when given random multi-variables are all hyperfinite.

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Authors and Affiliations

  1. Graduate School of Mathematics, Kyushu University, Fukuoka, 810-8560, Japan

    Yoshimichi Ueda

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  1. Yoshimichi Ueda
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Correspondence to Yoshimichi Ueda.

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Supported by Japan Society for the Promotion of Science (Grant-in-Aid for Challenging Exploratory Research 16K13762).

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Ueda, Y. A remark on orbital free entropy. Arch. Math. 108, 629–638 (2017). https://doi.org/10.1007/s00013-017-1035-2

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  • DOI: https://doi.org/10.1007/s00013-017-1035-2

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