Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture
Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Conférences de : P. Lelong, A. Lichnerowicz, E. Lieb et C. Stanojevic, Tome 19 (1973), Exposé no. 4, 36 p. 
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     author = {Lieb, Elliott H.},
     title = {Convex {Trace} {Functions} and the {Wigner-Yanase-Dyson} {Conjecture}},
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     note = {talk:4},
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     publisher = {Institut de Recherche Math\'ematique Avanc\'ee - Universit\'e Louis Pasteur},
     volume = {19},
     year = {1973},
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     url = {http://archive.numdam.org/item/RCP25_1973__19__A4_0/}
}
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Lieb, Elliott H. Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture. Les rencontres physiciens-mathématiciens de Strasbourg -RCP25, Conférences de : P. Lelong, A. Lichnerowicz, E. Lieb et C. Stanojevic, Tome 19 (1973), Exposé no. 4, 36 p. http://archive.numdam.org/item/RCP25_1973__19__A4_0/

[1.] E. P. Wigner and M. M. Yanase, Information Content of Distributions, Proc. Nat. Acad. Sci. U. S. A. 49 (1963), 910-918. | MR | Zbl

E. P. Wigner and M. M. Yanase On the Positive Semidefinite Nature of Certain Matrix Expressions, Canad. J. Math. 16 (1964), 397-406. | MR | Zbl

[2.] D. W. Robinson and D. Ruelle, Mean Entropy of States in Classical Statistical Mechanics, Commun. Math. Phys. 5 (1967), 288-300. | MR | Zbl

[3.] O. E. Lanford Iii and D. W. Robinson, Mean Entropy of States in Quantum Statistical Mechanics, J. Math. Phys. 9 (1968), 1120-1125. | Zbl

[4.] H. Araki and E. H. Lieb, Entropy Inequalities, Commun. Math. Phys. 18 (1970), 160-170. | MR

[5.] E. H. Lieb and M. B. Ruskai, Proof of the Strong Subadditivity of Quantum Mechanical Entropy, to be submitted to J. Math. Phys.

See aslo Property of Quantum Mechanical Entropy, Phys. Rev. Lett. (1973) to appear.

[6.] J. Bendat and S. Sherman, Monotone and Convex Operator Functions, Trans. Amer. Math. Soc. 79 (1955), 58-71. | MR | Zbl

F. Krauss, Math. Zeit. 41 (1936), 18.

[7.] R. T. Rockafellar, "Convex Analysis", Princeton University, Princeton, N.J. , 1970, cf. Theorem 15.3. | MR | Zbl

[8.] The idea of representing A1 in this manner is due to A. Uhlmann, Endlich Dimensionale Dichtematrizen II, preprint, submitted to Wissen. Z. Karl-Marx-Univ., Leipzig (1972).

[9.] P. Baumann, and R. Jost, Remarks on a Conjecture of Robinson and Ruelle Concerning the Quantum Mechanical Entropy, in "Problems of Theoretical Physics ; Essays Devoted to N. N. Bogoliubov", (1969), 285-293, Moscow, Nauka.

[10.] F. Baumann, Bemerkungen Ueber Quantenmechanische Entropie Ungleichungen, Helv. Phys. Acta 44 (1971), 95-100. | MR

[11.] S. Golden, Lower Bounds for the Helmhotz Function, Phys. Rev. 137 (1965) B 1127-1128. | MR | Zbl

[12.] C. J. Thompson, Inequality with Applications in Statistical Mechanics, J. Math. Phys. 6 (1965), 1812-1813. | MR

[13.] M. B. Ruskai, Inequalities for Traces on Von Neumann Algebras, Commun. Math. Phys. 26 (1972), 280-289. | MR | Zbl