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Orbital approach to microstate free entropy

Fumio Hiai·Takuho Miyamoto·Yoshimichi Ueda
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Abstract

Motivated by Voiculescu's liberation theory, we introduce the orbital free entropy $\chi_orb$ for non-commutative self-adjoint random variables (also for "hyperfinite random multi-variables"). Besides its basic properties the relation of $\chi_orb$ with the usual free entropy $\chi$ is shown. Moreover, the dimension counterpart $\delta_{0,orb}$ of $\chi_orb$ is discussed, and we obtain the relation of $\delta_{0,orb}$ with the original free entropy dimension $\delta_0$ with applications to $\delta_0$ itself.

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Fumio Hiai, Takuho Miyamoto, Yoshimichi Ueda. 2007-02-25. Orbital approach to microstate free entropy. https://doi.org/10.1142/s0129167x09005261

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