Concavification of free entropy
Operator Algebras
2012-11-13 v2 Probability
Abstract
We introduce a modification of Voiculescu's free entropy which coincides with the liminf variant of Voiculescu's free entropy on extremal states, but is a concave upper semi-continuous function on the trace state space. We also extend the orbital free entropy of Hiai, Miyamoto and Ueda to non-hyperfinite multivariables and prove freeness in case of additivity of Voiculescu's entropy (or vanishing of our extended orbital entropy).
Keywords
Cite
@article{arxiv.1201.0716,
title = {Concavification of free entropy},
author = {Philippe Biane and Yoann Dabrowski},
journal= {arXiv preprint arXiv:1201.0716},
year = {2012}
}
Comments
28 pages, final version : details added in several proofs and relations to other variants of free entropy explained