References
Ando, T.: Topics on operator inequalities. Lecture notes (mimeographed), Hokkaido Univ., Sapporo 1978
Bendat, J., Sherman, S.: Monotone and convex operator functions. Trans. Am. Math. Soc.79, 58–71 (1955)
Choi, M.-D.: A Schwarz inequality for positive linear maps onC *-algebras. Ill. J. Math.18, 565–574 (1974)
Davis, C.: A Schwarz inequality for convex operator functions. Proc. Am. Math. Soc.,8, 42–44 (1957)
Davis, C.: Notions generalizing convexity for functions defined on spaces of matrices. Proc. Am. Math. Soc. Symposia (Convexity)7, pp. 187–201 (1963)
Donoghue, W.: Monotone matrix functions and analytic continuation. Berlin, Heidelberg, New York: Springer 1974
Hansen, F.: An operator inequality. Math. Ann.246, 249–250 (1980)
Jensen, J.L.W.V.: Om Konvekse Funktioner og Uligheder mellem Middelværdier. Nyt Tidsskr. Math.B16, 49–68 (1905)
Jensen, J.L.W.V.: Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Math.30, 175–193 (1906)
Morányi, A.: On a theorem of Löwner and its connection with resolvents of self-adjoint transformations Acta Sci. Math. (Szeged)17, 63–70 (1956)
Löwner, K.: Über monotone Matrixfunktionen. Math. Z.38, 177–216 (1934)
Sz-Nagy, B.: Remarks to the preceeding paper of A. Korányi. Acta Sci. Math. (Szeged)17, 71–75 (1956)
Pedersen, G.K.:C *-algebras and their automorphism groups. London. Math. Soc. Monographs.14. London, New York: Academic Press 1979
Sparr, G.: A new proof of Löwner's theorem on monotone matrix functions. Math. Scand.47, 266–274 (1980)
Author information
Authors and Affiliations
Rights 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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01450679