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Lieb, Elliott H.

Convex trace functions and the Wigner-Yanase-Dyson conjecture. (English) Zbl 0267.46055

Adv. Math. 11, 267-288 (1973).
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Cited in 11 Reviews
Cited in 243 Documents

MSC:

46L99 Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)
15A45 Miscellaneous inequalities involving matrices
47A99 General theory of linear operators
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References:

[1] Wigner, E. P.; Yanase, M. M., On the positive semidefinite nature of certain matrix expressions, Canad. J. Math., 16, 397-406 (1964), See also · Zbl 0121.26203
[2] Robinson, D. W.; Ruelle, D., Mean entropy of states in classical statistical mechanics, Commun. Math. Phys., 5, 288-300 (1967) · Zbl 0144.48205
[3] Lanford, O. E.; Robinson, D. W., Mean entropy of states in quantum statistical mechanics, J. Math. Phys., 9, 1120-1125 (1968) · Zbl 0174.28303
[4] Araki, H.; Lieb, E. H., Entropy inequalities, Commun. Math. Phys., 18, 160-170 (1970)
[5] A fundamental property of quantum mechanical entropy. A fundamental property of quantum mechanical entropy, Phys. Rev. Lett., 30, 434-436 (1973), See also
[6] Krauss, F., Math. Z., 41, 18 (1936) · JFM 62.1079.02
[7] Rockaffllar, R. T., Convex Analysis (1970), Princeton University: Princeton University Princeton, NJ, cf. Theorem 15.3 · Zbl 0193.18401
[8] Uhlmann, A., Endlich Dimensionale Dichtermatrizen II, Wiss. Z. Karl-Marx-Univ. Leipzig Math.-Natur. Reihe, 22, H. 2, 139-177 (1973), Jg.
[9] Baumann, F.; Jost, R., Remarks on a conjecture of Robinson and Ruelle concerning the quantum mechanical entropy, (Problems of Theoretical Physics; Essays Devoted to N. N. Bogoliubov (1969), Nauka: Nauka Moscow), 285-293
[10] Baumann, F., Bemerkungen Ueber Quantenmechanische Entropie Ungleichungen, Helv. Phys. Acta, 44, 95-100 (1971)
[11] Golden, S., Lower bounds for the Helmhotz function, Phys. Rev., 137, B1127-B1128 (1965) · Zbl 0125.23204
[12] Thompson, C. J., Inequality with applications in statistical mechanics, J. Math. Phys., 6, 1812-1813 (1965)
[13] Breitenbecker, M.; Gruemm, H. R., Note on trace inequalities, Commun. Math. Phys., 26, 276-279 (1972) · Zbl 0254.47036
[14] Epstein, H., Remarks on two theorems of E. Lieb, Commun. Math. Phys., 31, 317-325 (1973) · Zbl 0257.46089
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