Orbital approach to microstate free entropy

Details Orbital approach to microstate free entropy Orbital approach to microstate free entropy

2007-02-25

arxiv.org/abs/math/0702745v3

Mathematics

Operator Algebras

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

Scientific paper

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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