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References
L. Accardi and G.S. Watson, these proceedings
T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Lin. Alg. Appl., 26 (1979), 203–241.
M. Araki, Golden-Thompson and Peierls-Bogoliubov inequalities for a general von Neumann algebra, Commun. Math. Phys., 34 (1973), 167–178.
F.A. Berezin, Covariant and contravariant symbols of operators (Russian), Izvez. Akad. Nauk SSSR Ser. Mat., 36 (1972), 1134–1156.
A. Berman and R.J. Plemmons, Nonnegative matrices in the mathematical sciences, Academic Press, 1979.
O. Bratteli and D.W. Robinson, Operator algebras and quantum statistical mechanics I, Springer-Verlag, 1979.
W. Cegla, J.T. Lewis and G.A. Raggio, The free energy of quantum systems and large deviations, to appear.
D. E. Evans and R. Hoegh-Krohn, Spectral properties of positive maps on C*-algebras, J. London Math. Soc., 17 (1978), 345–355.
S. Golden, Lower bounds for Helmholtz functions, Phys. Rev. 137 B (1965), 1127–1128.
U. Groh, Some observations on the spectra of positive operators on finite dimensional C*-algebras, Lin. Alg. Appl., 42 (1982), 213–222.
E.H. Lieb, The classical limit of quantum spin systems, Commun. Math. Phys., 31 (1973), 327–340.
D. Petz, Spectral scale of selfadjoint operators and trace inequalities, J. Math. Anal. Appl., 109 (1985), 74–82.
D. Petz, Jensen's inequality for contraction on operator algebras, Proc. Amer. Math. Soc., 99 (1987), 273–277.
D. Petz, A variational expression for the relative entropy, Commun. Math. Phys., 114 (1988), 345–349.
W. Pusz and S.L. Woronowicz, Functional calculus for sesquilinear forms and the purification map, Rep. Math. Phys., 8 (1975), 159–170.
H.H. Schaefer, Banach lattices and positive operators, Springer-Verlag, 1974.
C. Thompson, Inequality with application in statistical mechanics, J. Math. Phys., 6 (1965), 1812–1813.
C. Thompson, Inequalities and partial orders on matrix spaces, Indiana Univ. Math. J., 21 (1971), 469–480.
G.S. Watson, A method for discovering Kantorovich-type inequalities, Lin. Alg. Appl., 97 (1987), 211–220.
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Petz, D. (1989). Positive mappings on matrix algebras. In: Accardi, L., von Waldenfels, W. (eds) Quantum Probability and Applications IV. Lecture Notes in Mathematics, vol 1396. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083559
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DOI: https://doi.org/10.1007/BFb0083559
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