The noncommutative Hilbert transform approach to free entropy

Dan Voiculescu

Banach Center Publications (1998)

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

How to cite

top

Voiculescu, 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. [1] K. Dykema, Two applications of free entropy, preprint. Zbl0927.46035
  2. [2] L. Ge, Applications of free entropy to finite von Neumann algebras, I, American J. Math. 119 (1997), 467-485. Zbl0871.46031
  3. [3] L. Ge, Applications of free entropy to finite von Neumann algebras, II, Ann. of Math. 147 (1998), 143-157. Zbl0924.46050
  4. [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. [5] D. Voiculescu, Limit laws for random matrices and free products, Invent. Math. 104 (1991) 201-220. Zbl0736.60007
  6. [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. [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. [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. [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. [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. [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. [12] D. Voiculescu, K. Dykema and A. Nica, Free Random Variables, CRM Monograph Series, Vol. I, American Mathematical Society (1992). Zbl0795.46049

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.