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 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- December 1998
- DOI:
- 10.48550/arXiv.math/9812079
- arXiv:
- arXiv:math/9812079
- Bibcode:
- 1998math.....12079S
- Keywords:
-
- Operator Algebras;
- 46L50;
- 60H25