Remarks on free entropy dimension
| dc.creator | Shlyakhtenko, Dimitri | |
| dc.date | 2005-04-04 | |
| dc.date.accessioned | 2026-07-07T05:18:47Z | |
| dc.date.available | 2026-07-07T05:18:47Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0504062 | |
| dc.identifier | http://arxiv.org/abs/math/0504062 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74785 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L54 | |
| dc.title | Remarks on free entropy dimension | |
| dc.type | text |