Mathematische Annalen

, Volume 258, Issue 3, pp 229–241 | Cite as

Jensen's inequality for operators and Löwner's theorem

  • Frank Hansen
  • Gert Kjærgård Pedersen


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ando, T.: Topics on operator inequalities. Lecture notes (mimeographed), Hokkaido Univ., Sapporo 1978Google Scholar
  2. 2.
    Bendat, J., Sherman, S.: Monotone and convex operator functions. Trans. Am. Math. Soc.79, 58–71 (1955)Google Scholar
  3. 3.
    Choi, M.-D.: A Schwarz inequality for positive linear maps onC *-algebras. Ill. J. Math.18, 565–574 (1974)Google Scholar
  4. 4.
    Davis, C.: A Schwarz inequality for convex operator functions. Proc. Am. Math. Soc.,8, 42–44 (1957)Google Scholar
  5. 5.
    Davis, C.: Notions generalizing convexity for functions defined on spaces of matrices. Proc. Am. Math. Soc. Symposia (Convexity)7, pp. 187–201 (1963)Google Scholar
  6. 6.
    Donoghue, W.: Monotone matrix functions and analytic continuation. Berlin, Heidelberg, New York: Springer 1974Google Scholar
  7. 7.
    Hansen, F.: An operator inequality. Math. Ann.246, 249–250 (1980)Google Scholar
  8. 8.
    Jensen, J.L.W.V.: Om Konvekse Funktioner og Uligheder mellem Middelværdier. Nyt Tidsskr. Math.B16, 49–68 (1905)Google Scholar
  9. 9.
    Jensen, J.L.W.V.: Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Math.30, 175–193 (1906)Google Scholar
  10. 10.
    Morányi, A.: On a theorem of Löwner and its connection with resolvents of self-adjoint transformations Acta Sci. Math. (Szeged)17, 63–70 (1956)Google Scholar
  11. 11.
    Löwner, K.: Über monotone Matrixfunktionen. Math. Z.38, 177–216 (1934)CrossRefGoogle Scholar
  12. 12.
    Sz-Nagy, B.: Remarks to the preceeding paper of A. Korányi. Acta Sci. Math. (Szeged)17, 71–75 (1956)Google Scholar
  13. 13.
    Pedersen, G.K.:C *-algebras and their automorphism groups. London. Math. Soc. Monographs.14. London, New York: Academic Press 1979Google Scholar
  14. 14.
    Sparr, G.: A new proof of Löwner's theorem on monotone matrix functions. Math. Scand.47, 266–274 (1980)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Frank Hansen
    • 1
  • Gert Kjærgård Pedersen
    • 1
  1. 1.Department of MathematicsUniversityCopenhagen ØDenmark

Personalised recommendations