A Microstates Approach to Relative Free Entropy
Operator Algebras
2007-05-23 v1
Abstract
We define and study a relative free entropy quantity, analogous in its properties to Voiculescu's relative free entropy Chi^*(...:B). Our definition uses matricial microstates, unlike his definition, which involves non-commutative Hilbert transform. We prove a change of variable formula and certain maximization results for our quantity. We also exhibit a connection between the free entropy of a matrix with operator entries, relative to the algebra of scalar matrices, with the free entropy of the entries of the matrix.
Keywords
Cite
@article{arxiv.math/9812079,
title = {A Microstates Approach to Relative Free Entropy},
author = {Dimitri Shlyakhtenko},
journal= {arXiv preprint arXiv:math/9812079},
year = {2007}
}