Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture

Elliott H. Lieb

Recherche Coopérative sur Programme n°25 (1973)

  • Volume: 19, page 0-35

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Lieb, Elliott H.. "Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture." Recherche Coopérative sur Programme n°25 19 (1973): 0-35. <http://eudml.org/doc/274831>.

@article{Lieb1973,
author = {Lieb, Elliott H.},
journal = {Recherche Coopérative sur Programme n°25},
language = {eng},
pages = {0-35},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture},
url = {http://eudml.org/doc/274831},
volume = {19},
year = {1973},
}

TY - JOUR
AU - Lieb, Elliott H.
TI - Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture
JO - Recherche Coopérative sur Programme n°25
PY - 1973
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 19
SP - 0
EP - 35
LA - eng
UR - http://eudml.org/doc/274831
ER -

References

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  1. [1.] E. P. Wigner and M. M. Yanase, Information Content of Distributions, Proc. Nat. Acad. Sci.U. S. A.49 (1963), 910-918. Zbl0128.14104MR151127
  2. E. P. Wigner and M. M. YanaseOn the Positive Semidefinite Nature of Certain Matrix Expressions, Canad. J. Math.16 (1964), 397-406. Zbl0121.26203MR162810
  3. [2.] D. W. Robinson and D. Ruelle, Mean Entropy of States in Classical Statistical Mechanics, Commun. Math. Phys.5 (1967), 288-300. Zbl0144.48205MR225553
  4. [3.] O. E. Lanford III and D. W. Robinson, Mean Entropy of States in Quantum Statistical Mechanics, J. Math. Phys.9 (1968), 1120-1125. Zbl0174.28303
  5. [4.] H. Araki and E. H. Lieb, Entropy Inequalities, Commun. Math. Phys.18 (1970), 160-170. MR266563
  6. [5.] E. H. Lieb and M. B. Ruskai, Proof of the Strong Subadditivity of Quantum Mechanical Entropy, to be submitted to J. Math. Phys. 
  7. See aslo Property of Quantum Mechanical Entropy, Phys. Rev. Lett. (1973) to appear. 
  8. [6.] J. Bendat and S. Sherman, Monotone and Convex Operator Functions, Trans. Amer. Math. Soc.79 (1955), 58-71. Zbl0064.36901MR82655
  9. F. Krauss, Math. Zeit.41 (1936), 18. 
  10. [7.] R. T. Rockafellar, "Convex Analysis", Princeton University, Princeton, N.J. , 1970, cf. Theorem 15.3. Zbl0932.90001MR274683
  11. [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). 
  12. [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. 
  13. [10.] F. Baumann, Bemerkungen Ueber Quantenmechanische Entropie Ungleichungen, Helv. Phys. Acta44 (1971), 95-100. MR303895
  14. [11.] S. Golden, Lower Bounds for the Helmhotz Function, Phys. Rev.137 (1965) B 1127-1128. Zbl0125.23204MR189691
  15. [12.] C. J. Thompson, Inequality with Applications in Statistical Mechanics, J. Math. Phys.6 (1965), 1812-1813. MR189688
  16. [13.] M. B. Ruskai, Inequalities for Traces on Von Neumann Algebras, Commun. Math. Phys.26 (1972), 280-289. Zbl0257.46101MR312284

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