Some minimization problems for the free analogue of the Fisher information

Advances in Mathematics

Volumn 141, Issue 2, 1999, Pages 282-321

  Nica, Alexandru ^a   Shlyakhtenko, Dimitri ^b   Speicher, Roland ^c,d  

^a UNIVERSITY OF WATERLOO   (Canada)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF HEIDELBERG   (Germany)

^d Heisenberg Fellowship of the DFG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033540441     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1998.1780     Document Type: Article

References (9)

1. A. Nica and R. Speicher, R-diagonal pairs - A common approach to Haar unitaries and circular elements, Fields Inst. Commun. 12 (1997), 149-188.
2. D. Shlyakhtenko, Some applications of freeness with amalgamation, J. Reine Angew. Math. 500 (1998), 191-212.
3. D. Shlyakhtenko, Free Entropy with Respect to a Completely Positive Map, Preprint May 1998.
4. D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, I., Commun. Math. Phys. 155 (1993), 71-92.
5. D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, II., Invent. Math. 118 (1994), 411-440.
6. D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, III: The absence of Cartan subalgebras, Geom. Funct. Anal. 6 (1996), 172-199.
7. D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, IV: Maximum entropy and freeness, Fields Inst. Commun. 12 (1997), 293-302.
8. D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, V: Non-commutative Hilbert transforms, Invent. Math. 132 (1998), 189-227.
9. D. V. Voiculescu, K. J. Dykema, and A. Nica, "Free Random Variables," CRM Monograph Series, Vol. 1, American Mathematical Society, Providence, RI, 1992.