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Jensen’s inequality for operators and Loewner’s theorem. (English) Zbl 0473.47011


MSC:

47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
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References:

[1] Ando, T.: Topics on operator inequalities. Lecture notes (mimeographed), Hokkaido Univ., Sapporo 1978
[2] Bendat, J., Sherman, S.: Monotone and convex operator functions. Trans. Am. Math. Soc.79, 58-71 (1955) · Zbl 0064.36901 · doi:10.1090/S0002-9947-1955-0082655-4
[3] Choi, M.-D.: A Schwarz inequality for positive linear maps onC *-algebras. Ill. J. Math.18, 565-574 (1974) · Zbl 0293.46043
[4] Davis, C.: A Schwarz inequality for convex operator functions. Proc. Am. Math. Soc.,8, 42-44 (1957) · Zbl 0080.10505 · doi:10.1090/S0002-9939-1957-0084120-4
[5] Davis, C.: Notions generalizing convexity for functions defined on spaces of matrices. Proc. Am. Math. Soc. Symposia (Convexity)7, pp. 187-201 (1963) · Zbl 0196.30303
[6] Donoghue, W.: Monotone matrix functions and analytic continuation. Berlin, Heidelberg, New York: Springer 1974 · Zbl 0278.30004
[7] Hansen, F.: An operator inequality. Math. Ann.246, 249-250 (1980) · Zbl 0415.47015 · doi:10.1007/BF01371046
[8] Jensen, J.L.W.V.: Om Konvekse Funktioner og Uligheder mellem Middelv?rdier. Nyt Tidsskr. Math.B16, 49-68 (1905) · JFM 36.0447.03
[9] Jensen, J.L.W.V.: Sur les fonctions convexes et les in?galit?s entre les valeurs moyennes. Acta Math.30, 175-193 (1906) · JFM 37.0422.02 · doi:10.1007/BF02418571
[10] Mor?nyi, A.: On a theorem of L?wner and its connection with resolvents of self-adjoint transformations Acta Sci. Math. (Szeged)17, 63-70 (1956)
[11] L?wner, K.: ?ber monotone Matrixfunktionen. Math. Z.38, 177-216 (1934) · Zbl 0008.11301 · doi:10.1007/BF01170633
[12] Sz-Nagy, B.: Remarks to the preceeding paper of A. Kor?nyi. Acta Sci. Math. (Szeged)17, 71-75 (1956) · Zbl 0074.10203
[13] Pedersen, G.K.:C *-algebras and their automorphism groups. London. Math. Soc. Monographs.14. London, New York: Academic Press 1979 · Zbl 0416.46043
[14] Sparr, G.: A new proof of L?wner’s theorem on monotone matrix functions. Math. Scand.47, 266-274 (1980) · Zbl 0433.15012
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