TY - JOUR
T1 - Notes on microstate free entropy of projections
AU - Hiai, Fumio
AU - Ueda, Yoshimichi
PY - 2008/3
Y1 - 2008/3
N2 - We study the microstate free entropy χproj (p 1,... , pn) of projections, and establish its basic properties similar to the self-adjoint variable case. Our main contribution is to characterize the pair-block freeness of projections by the additivity of χproj (Theorem 4.1), in the proof of which a transportation cost inequality plays an important role. We also briefly discuss the free pressure in relation to χproj.
AB - We study the microstate free entropy χproj (p 1,... , pn) of projections, and establish its basic properties similar to the self-adjoint variable case. Our main contribution is to characterize the pair-block freeness of projections by the additivity of χproj (Theorem 4.1), in the proof of which a transportation cost inequality plays an important role. We also briefly discuss the free pressure in relation to χproj.
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U2 - 10.2977/prims/1207921076
DO - 10.2977/prims/1207921076
M3 - Article
AN - SCOPUS:44449164471
VL - 44
SP - 49
EP - 89
JO - Publications of the Research Institute for Mathematical Sciences
JF - Publications of the Research Institute for Mathematical Sciences
SN - 0034-5318
IS - 1
ER -