Orbital approach to microstate free entropy

Fumio Hiai; Takuho Miyamoto; Yoshimichi Ueda

doi:10.1142/S0129167X09005261

Orbital approach to microstate free entropy

算子代数 2019-05-21 v3 概率论

作者: Fumio Hiai , Takuho Miyamoto , Yoshimichi Ueda

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摘要

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.

引用

@article{arxiv.math/0702745,
  title  = {Orbital approach to microstate free entropy},
  author = {Fumio Hiai and Takuho Miyamoto and Yoshimichi Ueda},
  journal= {arXiv preprint arXiv:math/0702745},
  year   = {2019}
}

备注

38 pages; Section 5 was largely improved and Section 6 was added

Orbital approach to microstate free entropy

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