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Means and concave products of positive semi-definite matrices

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References

  1. Anderson, W.N., Jr., Duffin, R.J.: Series and parallel addition of matrices. J. Math. Anal. Appl.26, 576–594 (1969)

    Google Scholar 

  2. Anderson, W.N., Jr., Morley, D.E., Trapp, G.E.: Characterization of parallel sums. Proc. Natl. Acad. Sci. USA76, 3599–3601 (1979)

    Google Scholar 

  3. Anderson, W.N., Jr., Schreiber, M.: The infimum of two projections. Acta Sci. Math.33, 165–168 (1972)

    Google Scholar 

  4. Anderson, W.N., Jr., Trapp, G.E.: Shorted operators. II. SIAM J. Appl. Math.28, 60–71 (1975)

    Google Scholar 

  5. Ando, T.: Concavity of certain maps on positive definite matrices and applications to Hadamard products. Linear Algebra Appl.26, 203–241 (1979)

    Google Scholar 

  6. Araki, H.: Relative entropy of states of von Neumann algebras I, II. Publ. RIMS. Kyoto Univ.11, 809–833 (1975/76), and13, 173–192 (1977)

    Google Scholar 

  7. Bendat, J., Sherman, S.: Monotone and convex operator functions. Trans. Am. Math. Soc.79, 58–71 (1955)

    Google Scholar 

  8. Donoghue, W.: Monotone matrix functions and analytic continuation. Berlin, Heidelberg, New York: Springer 1974

    Google Scholar 

  9. Epstein, H.: Remarks on two theorems of E. Lieb. Comm. Math. Phys.31, 317–325 (1973)

    Google Scholar 

  10. Fujii, J.I.: Arithmetico-geometric mean of operators. Math. Japon.23, 667–669 (1979)

    Google Scholar 

  11. Fujii, J.I.: On geometric and harmonic means of operators. Math. Japon.24, 203–207 (1979)

    Google Scholar 

  12. Fujii, J.I.: Initial conditions on operator monotone functions. Math. Japon.24, 459–462 (1979)

    Google Scholar 

  13. Fujii, J.I., Fujii, M.: Some remarks on operator means. Math. Japon.24, 335–339 (1979)

    Google Scholar 

  14. Halmos, P.R.: A Hilbert space problem book. American Book 1967

  15. Hansen, F.: An operator inequality. Math. Ann.246, 249–250 (1980)

    Google Scholar 

  16. Hansen, F.: Selfadjoint means and operator monotone functions. Math. Ann.256, 29–35 (1981)

    Google Scholar 

  17. Hansen, F., Pedersen, G.K.: Jensen's inequality for operators and Löwner's theorem. Math. Ann.258, 229–241 (1982)

    Google Scholar 

  18. Kainuma, D., Nakamura, M.: Around Jensen's inequality. Math. Japon.25, 585–588 (1980)

    Google Scholar 

  19. Kosaki, H.: Interpolation theory and the Wigner-Yanase-Dyson-Lieb concavity. Comm. Math. Phys.87, 315–329 (1982)

    Google Scholar 

  20. Kubo, I., Ando, T.: Means of positive linear operators. Math. Ann.246, 205–224 (1980)

    Google Scholar 

  21. Lieb, E.: Convex trace functions and the Wigner-Yanase-Dyson conjecture. Adv. Math.11, 267–288 (1973)

    Google Scholar 

  22. Löwner, K.: Über monotone Matrixfunktionen. Math. Z.38, 177–216 (1934)

    Google Scholar 

  23. Nishio, K., Ando, T.: Characterizations of operations derived from network connections. J. Math. Anal. Appl.53, 539–549 (1976)

    Google Scholar 

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

    Google Scholar 

  25. Pusz, W., Woronowicz, S.L.: Form convex functions and the WYDL and other inequalities. Lett. Math. Phys.2, 505–512 (1978)

    Google Scholar 

  26. Uhlmann, A.: Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory. Comm. Math. Phys.54, 21–32 (1977)

    Google Scholar 

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Hansen, F. Means and concave products of positive semi-definite matrices. Math. Ann. 264, 119–128 (1983). https://doi.org/10.1007/BF01458054

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