Skip to main content
Log in

Jensen's inequality for operators and Löwner's theorem

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Ando, T.: Topics on operator inequalities. Lecture notes (mimeographed), Hokkaido Univ., Sapporo 1978

    Google Scholar 

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

    Google Scholar 

  3. Choi, M.-D.: A Schwarz inequality for positive linear maps onC *-algebras. Ill. J. Math.18, 565–574 (1974)

    Google Scholar 

  4. Davis, C.: A Schwarz inequality for convex operator functions. Proc. Am. Math. Soc.,8, 42–44 (1957)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  8. Jensen, J.L.W.V.: Om Konvekse Funktioner og Uligheder mellem Middelværdier. Nyt Tidsskr. Math.B16, 49–68 (1905)

    Google Scholar 

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

    Article  Google Scholar 

  12. Sz-Nagy, B.: Remarks to the preceeding paper of A. Korányi. Acta Sci. Math. (Szeged)17, 71–75 (1956)

    Google Scholar 

  13. Pedersen, G.K.:C *-algebras and their automorphism groups. London. Math. Soc. Monographs.14. London, New York: Academic Press 1979

    Google Scholar 

  14. Sparr, G.: A new proof of Löwner's theorem on monotone matrix functions. Math. Scand.47, 266–274 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hansen, F., Kjærgård Pedersen, G. Jensen's inequality for operators and Löwner's theorem. Math. Ann. 258, 229–241 (1982). https://doi.org/10.1007/BF01450679

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01450679

Navigation