A short note on relative entropy for a pair of intermediate subfactors
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- by Keshab Chandra Bakshi
- Proc. Amer. Math. Soc. 150 (2022), 3899-3913
- DOI: https://doi.org/10.1090/proc/16013
- Published electronically: May 20, 2022
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Abstract:
Given a quadruple of finite index subfactors we explicitly compute the Pimsner-Popa probabilistic constant for the pair of intermediate subfactors and relate it with the corresponding Connes-Størmer relative entropy between them. This generalizes an old result of Pimsner and Popa [Ann. Sci. École Norm. Sup. (4) 19 (1986), pp. 57–106].References
- Keshab Chandra Bakshi, Sayan Das, Zhengwei Liu, and Yunxiang Ren, An angle between intermediate subfactors and its rigidity, Trans. Amer. Math. Soc. 371 (2019), no. 8, 5973–5991. MR 3937315, DOI 10.1090/tran/7738
- Keshab Chandra Bakshi and Ved Prakash Gupta, A note on irreducible quadrilaterals of $II_1$ factors, Internat. J. Math. 30 (2019), no. 12, 1950061, 22. MR 4039099, DOI 10.1142/s0129167x19500617
- A. Connes and E. Størmer, Entropy for automorphisms of $II_{1}$ von Neumann algebras, Acta Math. 134 (1975), no. 3-4, 289–306. MR 454657, DOI 10.1007/BF02392105
- Chunlan Jiang, Zhengwei Liu, and Jinsong Wu, Noncommutative uncertainty principles, J. Funct. Anal. 270 (2016), no. 1, 264–311. MR 3419762, DOI 10.1016/j.jfa.2015.08.007
- V. F. R. Jones, Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. MR 696688, DOI 10.1007/BF01389127
- Sergey Neshveyev and Erling Størmer, Dynamical entropy in operator algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 50, Springer-Verlag, Berlin, 2006. MR 2251116, DOI 10.1007/978-3-540-34197-0
- Rui Okayasu, Relative entropy for abelian subalgebras, Internat. J. Math. 21 (2010), no. 4, 537–550. MR 2647454, DOI 10.1142/S0129167X10006148
- Mihai Pimsner and Sorin Popa, Entropy and index for subfactors, Ann. Sci. École Norm. Sup. (4) 19 (1986), no. 1, 57–106. MR 860811, DOI 10.24033/asens.1504
Bibliographic Information
- Keshab Chandra Bakshi
- Affiliation: Department of Mathematics, Chennai Mathematical Institute, Chennai, India
- MR Author ID: 1197952
- Email: bakshi209@gmail.com, kcbakshi@cmi.ac.in
- Received by editor(s): May 21, 2021
- Received by editor(s) in revised form: November 23, 2021
- Published electronically: May 20, 2022
- Additional Notes: The first author was supported through a DST INSPIRE Faculty grant (reference no. DST/INSPIRE/04/2019/002754).
- Communicated by: Adrian Ioana
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3899-3913
- MSC (2020): Primary 46L37
- DOI: https://doi.org/10.1090/proc/16013
- MathSciNet review: 4446239