Entropy and index for subfactors
Annales scientifiques de l'École Normale Supérieure (1986)
- Volume: 19, Issue: 1, page 57-106
- ISSN: 0012-9593
Access Full Article
topHow to cite
topPimsner, 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
top- [1] T. ANDO, Topics on Operator Inequalities (Lecture Notes, Saporo, 1978).
- [2] O. BRATTELI, Inductive Limits of Finite Dimensional C*-Algebras (Trans. Amer. Math Soc., Vol. 171, 1972, pp. 195-234). Zbl0264.46057MR312282
- [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] M. D. CHOI, A Schwartz Inequality for Positive Linear Maps (Canad. J. Math., 1975, pp. 559-574).
- [5] E. CHRISTENSEN, Subalgebras of a Finite Algebra (Math. Ann. Vol. 8, 1975, pp. 383-419). MR543091
- [7] A. CONNES, Classification of Injective Factors (Ann. of Math., Vol. 104, 1976, pp. 73-116). Zbl0343.46042MR454659
- [8] A. CONNES, Sur la classification des facteurs de type II (C. R. Acad. Sc., Paris, T. 281, 1975, pp. 383-420). Zbl0304.46042MR377534
- [9] A. CONNES et E. STÖRMER, Entropy for Automorphisms of II1, von Neumann Algebras (Acta Math., Vol. 134, 1975, pp. 288-306). Zbl0326.46032MR454657
- [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
- [11] C. DAVIS, A Schwartz Inequality for Convex Operator Functions (proc. Amer. Math. Soc., Vol. 8, 1957, pp. 42-44). Zbl0080.10505MR84120
- [12] M. GOLDMAN, On Subfactors of Factors of Type II1 (Mich. Math. J., Vol. 7, 1960, pp. 167-172). Zbl0121.10002MR107827
- [13] V. JONESIndex for Subfactors (Invent. Math., Vol. 72, 1983, pp. 1-25). Zbl0508.46040MR696688
- [14] R. V. KADISON, Problems on von Heumann Algebras, Baton Rouge, Conference, 1967.
- [15] F. KRAUS, Über konvexe Matrixfunctionen (Math. Z., Vol. 41, 1936, pp. 18-42). Zbl0013.39701JFM62.1079.02
- [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
- [17] K. LÖWNER, Über monotone matrixfunctionen (Math. Z., Vol. 38, 1934, pp. 117-216). Zbl0008.11301JFM60.0055.01
- [18] D. MCDUFF, Central Sequences and the Hyperfinite Factor (Proc. London Math. Soc., Vol. 21, 1970, pp. 443-461). Zbl0204.14902MR281018
- [19] F. MURRAY et J. VON NEUMANN, Rings of operators (Ann. of Math., Vol. 44, 1943, pp. 716-808). Zbl0060.26903MR9096
- [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
- [21] S. POPA, Orthogonal Pairs of Subalgebras in Finite von Neumann algebras (J. Operator Theory, Vol. 9, 1983, pp. 253-268). Zbl0521.46048MR703810
- [22] M. RIEFFEL, Induced Representations of C*-Algebras (Advances in Math., Vol. 13, 1974, pp. 176-257). Zbl0284.46040MR353003
- [23] S. SAKAI, C* and W*-Algebras (Ergebnisse der Math, und ihrer Grenzgebiete, Band 60). Zbl0219.46042MR442701
- [24] S. STRĂTILĂ et L. ZSIDO, Lectures on von Neumann Algebras, Abacus Press/Ed. Academiei, Tunbridge Wells/Bucuresti, 1979. Zbl0391.46048MR526399
- [25] H. UMEGAKI, Conditional Expectations in an Operator Algebra (Tohoku Math. J. Vol. 6, 1954, pp. 358-362). Zbl0058.10503
Citations in EuDML Documents
top- Michel Baillet, Yves Denizeau, Jean-François Havet, Indice d'une espérance conditionnelle
- Stefaan Vaes, Explicit computations of all finite index bimodules for a family of II factors
- Sergio Doplicher, Claudia Pinzari, Rita Zuccante, The -algebra of a Hilbert bimodule
- Vaughan Jones, Fusion en algèbres de von Neumann et groupes de lacets
- Sorin Popa, The relative Dixmier property for inclusions of von Neumann algebras of finite index
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.