Concavification of free entropy

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).

28 pages, final version : details added in several proofs and relations to other variants of free entropy explained

References in corpus (2)

• A Note about proving non-$\Gamma$ under a finite non-microstates free Fisher information Assumption
• Free analog of pressure and its Legendre transform

Cited by in corpus (1)

• The Bootstrap and von Neumann algebras: The Maximal Intersection Lemma