# The noncommutative Hilbert transform approach to free entropy

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 421-427
- ISSN: 0137-6934

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topVoiculescu, Dan. "The noncommutative Hilbert transform approach to free entropy." Banach Center Publications 43.1 (1998): 421-427. <http://eudml.org/doc/208863>.

@article{Voiculescu1998,

author = {Voiculescu, Dan},

journal = {Banach Center Publications},

keywords = {noncommutative Hilbert transform; free entropy; free independence; noncommutative random variables; tracial -probability space; matricial microstates; matrix-approximants; type von Neumann algebras; microstates approach; asymptotic freeness; random matrices},

language = {eng},

number = {1},

pages = {421-427},

title = {The noncommutative Hilbert transform approach to free entropy},

url = {http://eudml.org/doc/208863},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Voiculescu, Dan

TI - The noncommutative Hilbert transform approach to free entropy

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 421

EP - 427

LA - eng

KW - noncommutative Hilbert transform; free entropy; free independence; noncommutative random variables; tracial -probability space; matricial microstates; matrix-approximants; type von Neumann algebras; microstates approach; asymptotic freeness; random matrices

UR - http://eudml.org/doc/208863

ER -

## References

top- [1] K. Dykema, Two applications of free entropy, preprint. Zbl0927.46035
- [2] L. Ge, Applications of free entropy to finite von Neumann algebras, I, American J. Math. 119 (1997), 467-485. Zbl0871.46031
- [3] L. Ge, Applications of free entropy to finite von Neumann algebras, II, Ann. of Math. 147 (1998), 143-157. Zbl0924.46050
- [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. Zbl0863.46042
- [5] D. Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1991) 201-220. Zbl0736.60007
- [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. Zbl0895.60004
- [7] D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, Commun. Math. Phys. 155 (1993), 71-92. Zbl0781.60006
- [8] D. Voiculescu, The analogues of entropy and of Fisher's information measure in free probability theory, II, Invent. Math. 118 (1994), 411-440. Zbl0820.60001
- [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. Zbl0856.60012
- [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). Zbl0856.60012
- [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. Zbl0930.46053
- [12] D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, CRM Monograph Series, Vol. I, American Mathematical Society (1992). Zbl0795.46049

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