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Positive mappings on matrix algebras

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Quantum Probability and Applications IV

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1396))

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References

  1. L. Accardi and G.S. Watson, these proceedings

    Google Scholar 

  2. T. Ando, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Lin. Alg. Appl., 26 (1979), 203–241.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Araki, Golden-Thompson and Peierls-Bogoliubov inequalities for a general von Neumann algebra, Commun. Math. Phys., 34 (1973), 167–178.

    Article  MathSciNet  MATH  Google Scholar 

  4. F.A. Berezin, Covariant and contravariant symbols of operators (Russian), Izvez. Akad. Nauk SSSR Ser. Mat., 36 (1972), 1134–1156.

    MathSciNet  Google Scholar 

  5. A. Berman and R.J. Plemmons, Nonnegative matrices in the mathematical sciences, Academic Press, 1979.

    Google Scholar 

  6. O. Bratteli and D.W. Robinson, Operator algebras and quantum statistical mechanics I, Springer-Verlag, 1979.

    Google Scholar 

  7. W. Cegla, J.T. Lewis and G.A. Raggio, The free energy of quantum systems and large deviations, to appear.

    Google Scholar 

  8. D. E. Evans and R. Hoegh-Krohn, Spectral properties of positive maps on C*-algebras, J. London Math. Soc., 17 (1978), 345–355.

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Golden, Lower bounds for Helmholtz functions, Phys. Rev. 137 B (1965), 1127–1128.

    Article  MathSciNet  Google Scholar 

  10. U. Groh, Some observations on the spectra of positive operators on finite dimensional C*-algebras, Lin. Alg. Appl., 42 (1982), 213–222.

    Article  MathSciNet  MATH  Google Scholar 

  11. E.H. Lieb, The classical limit of quantum spin systems, Commun. Math. Phys., 31 (1973), 327–340.

    Article  MathSciNet  MATH  Google Scholar 

  12. D. Petz, Spectral scale of selfadjoint operators and trace inequalities, J. Math. Anal. Appl., 109 (1985), 74–82.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. Petz, Jensen's inequality for contraction on operator algebras, Proc. Amer. Math. Soc., 99 (1987), 273–277.

    MathSciNet  MATH  Google Scholar 

  14. D. Petz, A variational expression for the relative entropy, Commun. Math. Phys., 114 (1988), 345–349.

    Article  MathSciNet  MATH  Google Scholar 

  15. W. Pusz and S.L. Woronowicz, Functional calculus for sesquilinear forms and the purification map, Rep. Math. Phys., 8 (1975), 159–170.

    Article  MathSciNet  MATH  Google Scholar 

  16. H.H. Schaefer, Banach lattices and positive operators, Springer-Verlag, 1974.

    Google Scholar 

  17. C. Thompson, Inequality with application in statistical mechanics, J. Math. Phys., 6 (1965), 1812–1813.

    Article  Google Scholar 

  18. C. Thompson, Inequalities and partial orders on matrix spaces, Indiana Univ. Math. J., 21 (1971), 469–480.

    Article  MathSciNet  MATH  Google Scholar 

  19. G.S. Watson, A method for discovering Kantorovich-type inequalities, Lin. Alg. Appl., 97 (1987), 211–220.

    Article  MathSciNet  MATH  Google Scholar 

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Luigi Accardi Wilhelm von Waldenfels

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© 1989 Springer-Verlag

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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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51613-2

  • Online ISBN: 978-3-540-46713-7

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