The noncommutative Hilbert transform approach to free entropy

• Autorzy: Dan Voiculescu
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1998
• Tom: 43
• Numer: 1
• Strony: 421-427

Daty

wydano

1998

Twórcy

autor

Dan Voiculescu

• Department of Mathematics, University of California, Berkeley, California 94720-3840, U.S.A.

Bibliografia

• [1] K. Dykema, Two applications of free entropy, preprint.
• [2] L. Ge, Applications of free entropy to finite von Neumann algebras, I, American J. Math. 119 (1997), 467-485.
• [3] L. Ge, Applications of free entropy to finite von Neumann algebras, II, Ann. of Math. 147 (1998), 143-157.
• [4] S. J. Szarek and D. Voiculescu, Volumes of restricted Minkowski sums and the free analogue of the entropy power inequality, Commun. Math. Phys. 178 (1996) 563-570.
• [5] D. Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1991) 201-220.
• [6] D. Voiculescu, A strengthened asymptotic freeness result for random matrices with applications to free entropy, Internat. Math. Res. Notices 1998, no. 1, 41-63.
• [7] D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, Commun. Math. Phys. 155 (1993), 71-92.
• [8] D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, II, Invent. Math. 118 (1994), 411-440.
• [9] D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, III: the absence of Cartan subalgebras, Geometric and Functional Analysis, vol. 6, no. 1 (1996), 172-199.
• [10] D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, IV: maximum entropy and freeness, in: Free Probability, D. Voiculescu (ed.), Fields Institute Communications, Vol. 12, American Mathematical Society, Providence (1996).
• [11] D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, V: noncommutative Hilbert transforms, Invent. Math. 132 (1998), 189-227.
• [12] D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, CRM Monograph Series, Vol. I, American Mathematical Society (1992).