메뉴 건너뛰기




Volumn 202, Issue 2, 1999, Pages 421-444

Properties of free entropy related to polar decomposition

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033238571     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050589     Document Type: Article
Times cited : (7)

References (19)
  • 1
    • 0031499009 scopus 로고    scopus 로고
    • Large deviation for Wigner's law and Voiculescu's noncommutative entropy
    • 1. Ben Arous, G. and Guionnet, A.: Large deviation for Wigner's law and Voiculescu's noncommutative entropy. Prob. Theory Rel. Fields 108, 517-542 (1997)
    • (1997) Prob. Theory Rel. Fields , vol.108 , pp. 517-542
    • Ben Arous, G.1    Guionnet, A.2
  • 3
    • 0032221988 scopus 로고    scopus 로고
    • Maximizing free entropy
    • 3. Hiai, F. and Petz, D.: Maximizing free entropy. Acta Math. Hungar. 80, 335-356 (1998)
    • (1998) Acta Math. Hungar. , vol.80 , pp. 335-356
    • Hiai, F.1    Petz, D.2
  • 8
    • 0033540441 scopus 로고    scopus 로고
    • Some maximization problems for the free analogue of the Fisher information
    • To appear in
    • 8. Nica, A., Shlyakhtenko, D. and Speicher, R.: Some maximization problems for the free analogue of the Fisher information. To appear in Adv. Math.
    • Adv. Math.
    • Nica, A.1    Shlyakhtenko, D.2    Speicher, R.3
  • 9
    • 0001102352 scopus 로고    scopus 로고
    • R-diagonal pairs - A common approach to Haar unitaries and circular elements
    • D.V. Voiculescu (ed.), Fields Institute Communications, Providence, RI: Am. Math. Soc
    • 9. Nica, A. and Speicher, R.: R-diagonal pairs - A common approach to Haar unitaries and circular elements. In: Free Probability Theory, D.V. Voiculescu (ed.), Fields Institute Communications, Vol. 12, Providence, RI: Am. Math. Soc, 1997, pp. 149-188
    • (1997) Free Probability Theory , vol.12 , pp. 149-188
    • Nica, A.1    Speicher, R.2
  • 10
    • 0000159713 scopus 로고    scopus 로고
    • Logarithmic energy as entropy functional
    • Advances in Differential Equations and Mathematical Physics, E. Carlen et al. (eds.), Providence, RI: Am. Math. Soc.
    • 10. Petz, D. and Hiai, F.: Logarithmic energy as entropy functional. In: Advances in Differential Equations and Mathematical Physics, E. Carlen et al. (eds.), Contemp. Math. Vol. 217, Providence, RI: Am. Math. Soc., 1998, pp. 205-221
    • (1998) Contemp. Math. , vol.217 , pp. 205-221
    • Petz, D.1    Hiai, F.2
  • 11
    • 0000215544 scopus 로고
    • Limit laws for random matrices and free products
    • 11. Voiculescu, D.: Limit laws for random matrices and free products. Invent. Math. 104, 201-220 (1991)
    • (1991) Invent. Math. , vol.104 , pp. 201-220
    • Voiculescu, D.1
  • 12
    • 21144462319 scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory
    • 12. Voiculescu, D.: The analogues of entropy and of Fisher's information measure in free probability theory, I. Commun. Math. Phys. 155, 71-92 (1993)
    • (1993) I. Commun. Math. Phys. , vol.155 , pp. 71-92
    • Voiculescu, D.1
  • 13
    • 0000523766 scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory
    • 13. Voiculescu, D.: The analogues of entropy and of Fisher's information measure in free probability theory, II. Invent. Math. 118, 411-440 (1994)
    • (1994) II. Invent. Math. , vol.118 , pp. 411-440
    • Voiculescu, D.1
  • 14
    • 0030544382 scopus 로고    scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory, III: The absence of Cartan subalgebras
    • 14. Voiculescu, D.: The analogues of entropy and of Fisher's information measure in free probability theory, III: The absence of Cartan subalgebras. Geom. Funct. Anal. 6, 172-199 (1996)
    • (1996) Geom. Funct. Anal. , vol.6 , pp. 172-199
    • Voiculescu, D.1
  • 15
    • 0000824331 scopus 로고    scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory, IV: Maximum entropy and freeness
    • D.V. Voiculescu (ed.), Fields Institute Communications, Providence, RI: Am. Math. Soc.
    • 15. Voiculescu, D.: The analogues of entropy and of Fisher's information measure in free probability theory, IV: Maximum entropy and freeness. In: Free Probability Theory, D.V. Voiculescu (ed.), Fields Institute Communications, Vol. 12, Providence, RI: Am. Math. Soc., 1997, pp. 293-302
    • (1997) Free Probability Theory , vol.12 , pp. 293-302
    • Voiculescu, D.1
  • 16
    • 0032380955 scopus 로고    scopus 로고
    • The analogues of entropy and of Fisher's information measure in free probability theory, V: Noncommutative Hilbert transforms
    • 16. Voiculescu, D.: The analogues of entropy and of Fisher's information measure in free probability theory, V: Noncommutative Hilbert transforms. Invent. Math. 132, 189-227 (1998)
    • (1998) Invent. Math. , vol.132 , pp. 189-227
    • Voiculescu, D.1
  • 17
    • 1842679304 scopus 로고    scopus 로고
    • A strengthened asymptotic freeness result for random matrices with applications to free entropy
    • 17. Voiculescu, D.: A strengthened asymptotic freeness result for random matrices with applications to free entropy. Internat. Math. Res. Notices 41-63 (1998)
    • (1998) Internat. Math. Res. Notices , pp. 41-63
    • Voiculescu, D.1
  • 19
    • 0008976827 scopus 로고    scopus 로고
    • Maximality of the microstates free entropy for R-diagonal elements
    • To appear in
    • 19. Nica, A., Shlyakhtenko, D. and Speicher, R.: Maximality of the microstates free entropy for R-diagonal elements. To appear in Pacific J. Math.
    • Pacific J. Math.
    • Nica, A.1    Shlyakhtenko, D.2    Speicher, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.