Orbital approach to microstate free entropy

Fumio Hiai, Takuho Miyamoto, Yoshimichi Ueda

    Research output: Contribution to journalArticlepeer-review

    16 Citations (Scopus)


    Motivated by Voiculescu's liberation theory, we introduce the orbital free entropy χorb for non-commutative self-adjoint random variables (also for "hyperfinite random multi-variables"). Besides its basic properties, the relation of χorb with the usual free entropy χ is shown. Moreover, the dimension counterpart δ0,orb of χorb is discussed, and we obtain the relation between δ0,orb and the original free entropy dimension δ0 together with applications to δ0 itself.

    Original languageEnglish
    Pages (from-to)227-273
    Number of pages47
    JournalInternational Journal of Mathematics
    Issue number2
    Publication statusPublished - Feb 2009

    All Science Journal Classification (ASJC) codes

    • General Mathematics


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