2005/04/04 by Dimitri Shlyakhtenko, Shlyakhtenko, Dimitri
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #math.OA #msc:46L54
paper · pdf · doi:10.48550/arxiv.math/0504062
arxiv created 2005/04/04 · arxiv updated 2009/12/01
We prove a technical result, showing that the existence of a closable unbounded dual system in the sense of Voiculescu is equivalent to the finiteness of free Fisher information. This approach allows one to give a purely operator-algebraic proof of the computation of the non-microstates free entropy dimension for generators of groups carried out in an earlier joint work with I. Mineyev. The same technique also works for finite-dimensional algebras. We also show that Voiculescu's question of semi-continuity of free entropy dimension, as stated, admits a counterexample. We state a modified version of the question, which avoids the counterexample, but answering which in the affirmative would still imply the non-isomorphism of free group factors.