Commuting squares and a new relative entropy

Yuki SEO

doi:10.2969/jmsj/04920329

Yuki SEO

Author information

JOURNAL FREE ACCESS

1997 Volume 49 Issue 2 Pages 329-337

DOI https://doi.org/10.2969/jmsj/04920329

Details

Published: 1997 Received: August 25, 1994 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) V. P. Belavkin and P. Staszewski, C^*-algebraic generalization of relative entropy and entropy, Ann. Inst. H. Poincaré, 37 (1982), 51-58.
2) P. Bilingsly, Ergodic Theory and Information, Wiley Sons, 1965.
3) A. Connes and E. Størmer, Entropy for automorphisms of II₁ von Neumann algebras,Acta. Math., 134 (1975), 288-306.
4) J. I. Fujii, M. Fujii and Y. Seo, An extension of the Kubo-Ando theory: Solidarities, Math. Japon., 35 (1990), 387-396.
5) J. I. Fujii and E. Kamei, Relative operator entropy in noncommutative information theory, Math. Japon., 34 (1989), 341-348.
6) F. Goodman, P. de la Harpe and V. F. R. Jones, Coxeter Graphs and Towers of Algebras, Springer-Verlag, 1989.
7) F. Hiai, Minimum index for subfactors and entropy, J. Operator Theory, 24 (1990), 301-336.
8) F. Hiai, Minimum index for subfactors and entropy, II, J. Math Soc. Japan, 43 (1991), 347-379.
9) F. Hiai, Relative Hamiltonian and relative entropy, preliminary version.
10) F. Hiai and D. Petz, The proper formula for relative entropy and asymptotics in quantum probability, Comm. Math. Phys., 143 (1991), 99-114.
11) V. F. R. Jones, Index for subfactors, Invent. Math., 72 (1983), 1-25.
12) M. Nakamura and H. Umegaki, A note on the entropy for operator algebras, Proc. Japan Acad., 37 (1961), 149-154.
13) M. Pimsner and S. Popa, Entropy and index for subfactors, Ann. Sci. École Norm. Sup., 19 (1986), 57-106.
14) T. Sano and Y. Watatani, Angles between two subfactors, J. Operator Theory, 32 (1994), 209-241.
15) Y. Seo, A new relative entropy for von Neumann algebras, Math. Japon., 36 (1991), 51-57.
16) Y. Seo, Relative entropy for finite von Neumann algebras, J. Operator Theory, 29 (1993), 373-387.
17) M. Takesaki, Theory of Operator Algebras I, Springer-Verlag, 1979.
18) H. Umegaki, Conditional expectation in an operator algebra, Kôdai Math. Sem. Rep., 14 (1962), 59-85.
19) H. Umegaki and M. Ohya, Quantum Mechanical Entropies (in Japanese), Kyoritsu Publishing Company, 1984.
20) Y. Watatani and J. Wierzbicki, Commuting square and relative entropy for two subfactors, to appear in J. Funct. Anal.

Right : [1] V. P. Belavkin and P. Staszewski, C^*-algebraic generalization of relative entropy and entropy, Ann. Inst. H. Poincaré, 37 (1982), 51-58.
[2] P. Bilingsly, Ergodic Theory and Information, Wiley Sons, 1965.
[3] A. Connes and E. Størmer, Entropy for automorphisms of II₁ von Neumann algebras, Acta. Math., 134 (1975), 288-306.
[4] J. I. Fujii, M. Fujii and Y. Seo, An extension of the Kubo-Ando theory: Solidarities, Math. Japon., 35 (1990), 387-396.
[5] J. I. Fujii and E. Kamei, Relative operator entropy in noncommutative information theory, Math. Japon., 34 (1989), 341-348.
[6] F. Goodman, P. de la Harpe and V. F. R. Jones, Coxeter Graphs and Towers of Algebras, Springer-Verlag, 1989.
[7] F. Hiai, Minimum index for subfactors and entropy, J. Operator Theory, 24 (1990), 301-336.
[8] F. Hiai, Minimum index for subfactors and entropy, II, J. Math Soc. Japan, 43 (1991), 347-379.
[9] F. Hiai, Relative Hamiltonian and relative entropy, preliminary version.
[10] F. Hiai and D. Petz, The proper formula for relative entropy and asymptotics in quantum probability, Comm. Math. Phys., 143 (1991), 99-114.
[11] V. F. R. Jones, Index for subfactors, Invent. Math., 72 (1983), 1-25.
[12] M. Nakamura and H. Umegaki, A note on the entropy for operator algebras, Proc. Japan Acad., 37 (1961), 149-154.
[13] M. Pimsner and S. Popa, Entropy and index for subfactors, Ann. Sci. École Norm. Sup., 19 (1986), 57-106.
[14] T. Sano and Y. Watatani, Angles between two subfactors, J. Operator Theory, 32 (1994), 209-241.
[15] Y. Seo, A new relative entropy for von Neumann algebras, Math. Japon., 36 (1991), 51-57.
[16] Y. Seo, Relative entropy for finite von Neumann algebras, J. Operator Theory, 29 (1993), 373-387.
[17] M. Takesaki, Theory of Operator Algebras I, Springer-Verlag, 1979.
[18] H. Umegaki, Conditional expectation in an operator algebra, Kôdai Math. Sem. Rep., 14 (1962), 59-85.
[19] H. Umegaki and M. Ohya, Quantum Mechanical Entropies (in Japanese), Kyoritsu Publishing Company, 1984.
[20] Y. Watatani and J. Wierzbicki, Commuting square and relative entropy for two subfactors, to appear in J. Funct. Anal..

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!