TY - JOUR
T1 - Orbital approach to microstate free entropy
AU - Hiai, Fumio
AU - Miyamoto, Takuho
AU - Ueda, Yoshimichi
PY - 2009/2
Y1 - 2009/2
N2 - 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.
AB - 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.
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U2 - 10.1142/S0129167X09005261
DO - 10.1142/S0129167X09005261
M3 - Article
AN - SCOPUS:65249171927
SN - 0129-167X
VL - 20
SP - 227
EP - 273
JO - International Journal of Mathematics
JF - International Journal of Mathematics
IS - 2
ER -