R-diagonal elements and freeness with amalgamation

Canadian Journal of Mathematics

Volumn 53, Issue 2, 2001, Pages 355-381

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

^a UNIVERSITY OF WATERLOO   (Canada)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035626117     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-2001-015-6     Document Type: Article

References (13)

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3. _, Maximality of the microstates free entropy for R-diagonal elements. Pacific J. Math. 187(1999), 333-347.
4. A. Nica and R. Speicher, A "Fourier transform" for multiplicative functions on non-crossing partitions. J. Algebraic Combin. 6(1997), 141-160.
5. _, R-diagonal pairs - a common approach to Haar unitaries and circular elements. In: Free Probability Theory (ed. D. V. Voiculescu), Fields Inst. Comm. 12(1997), 149-188.
6. _, Commutators of free random variables. Duke Math. J. 92(1998), 553-592.
7. D. Shlyakhtenko, Free quasi-free states. Pacific J. Math. 177(1997), 329-368.
8. _, Some applications of freeness with amalgamation. J. Reine Angew. Math. 500(1998), 191-212.
9. R. Speicher, Multiplicative functions on the lattice of non-crossing partitions and free convolution. Math. Ann. 298(1994), 193-206.
10. _, Combinatorial theory of the free product with amalgamation and operator-valued free probability theory. Mem. Amer. Math. Soc. 132(1998), x+88.
11. D. V. Voiculescu, Circular and semicircular systems and free product factors. In: Operator algebras, unitary representations, enveloping algebras, and invariant theory, Progress in Math. 92, (eds., A. Connes et al.), Birkhäuser, Boston, 1990, 45-60.
12. _, The analogues of entropy and of Fisher's information measure in free probability theory, VI: Liberation and mutual free information. Adv. in Math. 146(1999), 101-166.
13. D. V. Voiculescu, K. J. Dykema and A. Nica, Free random variables. CRM Monograph Series 1, Amer. Math. Soc., Providence, 1992.