A Microstates Approach to Relative Free Entropy
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 noncommutative 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1998
 DOI:
 10.48550/arXiv.math/9812079
 arXiv:
 arXiv:math/9812079
 Bibcode:
 1998math.....12079S
 Keywords:

 Operator Algebras;
 46L50;
 60H25