Entropy and index for subfactors

Mihai Pimsner; Sorin Popa

Annales scientifiques de l'École Normale Supérieure (1986)

  • Volume: 19, Issue: 1, page 57-106
  • ISSN: 0012-9593

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Pimsner, Mihai, and Popa, Sorin. "Entropy and index for subfactors." Annales scientifiques de l'École Normale Supérieure 19.1 (1986): 57-106. <http://eudml.org/doc/82174>.

@article{Pimsner1986,
author = {Pimsner, Mihai, Popa, Sorin},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Jones index; finite von Neumann factors; trace preserving conditional expection; relative entropy; Jones' pair of subfactors},
language = {eng},
number = {1},
pages = {57-106},
publisher = {Elsevier},
title = {Entropy and index for subfactors},
url = {http://eudml.org/doc/82174},
volume = {19},
year = {1986},
}

TY - JOUR
AU - Pimsner, Mihai
AU - Popa, Sorin
TI - Entropy and index for subfactors
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1986
PB - Elsevier
VL - 19
IS - 1
SP - 57
EP - 106
LA - eng
KW - Jones index; finite von Neumann factors; trace preserving conditional expection; relative entropy; Jones' pair of subfactors
UR - http://eudml.org/doc/82174
ER -

References

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  1. [1] T. ANDO, Topics on Operator Inequalities (Lecture Notes, Saporo, 1978). 
  2. [2] O. BRATTELI, Inductive Limits of Finite Dimensional C*-Algebras (Trans. Amer. Math Soc., Vol. 171, 1972, pp. 195-234). Zbl0264.46057MR312282
  3. [3] M. CHODA, The Crossed Product of a Full II1-Factor by a Group of Outer Automorphisms (Math. Japonica, Vol. 23, No. 4, 1978, pp. 385-391). Zbl0395.46047MR524989
  4. [4] M. D. CHOI, A Schwartz Inequality for Positive Linear Maps (Canad. J. Math., 1975, pp. 559-574). 
  5. [5] E. CHRISTENSEN, Subalgebras of a Finite Algebra (Math. Ann. Vol. 8, 1975, pp. 383-419). MR543091
  6. [7] A. CONNES, Classification of Injective Factors (Ann. of Math., Vol. 104, 1976, pp. 73-116). Zbl0343.46042MR454659
  7. [8] A. CONNES, Sur la classification des facteurs de type II (C. R. Acad. Sc., Paris, T. 281, 1975, pp. 383-420). Zbl0304.46042MR377534
  8. [9] A. CONNES et E. STÖRMER, Entropy for Automorphisms of II1, von Neumann Algebras (Acta Math., Vol. 134, 1975, pp. 288-306). Zbl0326.46032MR454657
  9. [10] A. CONNES et E. STÖRMER, A Connection between the Classical and the Quantum Mechanical Entropies, in Operator Algebras and Group Representations, Pitman, 1983, pp. 113-123. Zbl0543.46040MR731767
  10. [11] C. DAVIS, A Schwartz Inequality for Convex Operator Functions (proc. Amer. Math. Soc., Vol. 8, 1957, pp. 42-44). Zbl0080.10505MR84120
  11. [12] M. GOLDMAN, On Subfactors of Factors of Type II1 (Mich. Math. J., Vol. 7, 1960, pp. 167-172). Zbl0121.10002MR107827
  12. [13] V. JONESIndex for Subfactors (Invent. Math., Vol. 72, 1983, pp. 1-25). Zbl0508.46040MR696688
  13. [14] R. V. KADISON, Problems on von Heumann Algebras, Baton Rouge, Conference, 1967. 
  14. [15] F. KRAUS, Über konvexe Matrixfunctionen (Math. Z., Vol. 41, 1936, pp. 18-42). Zbl0013.39701JFM62.1079.02
  15. [16] E. LIEB et M. B. RUSKAI, Proof of the Astrong Subaditivity of Quantum Mechanical Entropy (J. Math. Phys., Vol. 14, 1973, pp. 1938-1941). MR345558
  16. [17] K. LÖWNER, Über monotone matrixfunctionen (Math. Z., Vol. 38, 1934, pp. 117-216). Zbl0008.11301JFM60.0055.01
  17. [18] D. MCDUFF, Central Sequences and the Hyperfinite Factor (Proc. London Math. Soc., Vol. 21, 1970, pp. 443-461). Zbl0204.14902MR281018
  18. [19] F. MURRAY et J. VON NEUMANN, Rings of operators (Ann. of Math., Vol. 44, 1943, pp. 716-808). Zbl0060.26903MR9096
  19. [20] S. POPA, On a problem of R.V. Kadison on maximal abelian subalgebras in factors (Invent. math., Vol. 65, 1981, pp. 269-281). Zbl0481.46028MR641131
  20. [21] S. POPA, Orthogonal Pairs of Subalgebras in Finite von Neumann algebras (J. Operator Theory, Vol. 9, 1983, pp. 253-268). Zbl0521.46048MR703810
  21. [22] M. RIEFFEL, Induced Representations of C*-Algebras (Advances in Math., Vol. 13, 1974, pp. 176-257). Zbl0284.46040MR353003
  22. [23] S. SAKAI, C* and W*-Algebras (Ergebnisse der Math, und ihrer Grenzgebiete, Band 60). Zbl0219.46042MR442701
  23. [24] S. STRĂTILĂ et L. ZSIDO, Lectures on von Neumann Algebras, Abacus Press/Ed. Academiei, Tunbridge Wells/Bucuresti, 1979. Zbl0391.46048MR526399
  24. [25] H. UMEGAKI, Conditional Expectations in an Operator Algebra (Tohoku Math. J. Vol. 6, 1954, pp. 358-362). Zbl0058.10503

Citations in EuDML Documents

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  1. Qiaoling Xin, Tianqing Cao, C * -basic construction between non-balanced quantum doubles
  2. Michel Baillet, Yves Denizeau, Jean-François Havet, Indice d'une espérance conditionnelle
  3. Stefaan Vaes, Explicit computations of all finite index bimodules for a family of II 1 factors
  4. Sergio Doplicher, Claudia Pinzari, Rita Zuccante, The C * -algebra of a Hilbert bimodule
  5. Vaughan Jones, Fusion en algèbres de von Neumann et groupes de lacets
  6. Sorin Popa, The relative Dixmier property for inclusions of von Neumann algebras of finite index

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