A short note on relative entropy for a pair of intermediate subfactors

Bakshi, Keshab

doi:10.1090/proc/16013

A short note on relative entropy for a pair of intermediate subfactors
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by Keshab Chandra Bakshi PDF

Proc. Amer. Math. Soc. 150 (2022), 3899-3913 Request permission

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