Some operator inequalities
Séminaire de probabilités de Strasbourg, Tome 28 (1994), pp. 316-333.
@article{SPS_1994__28__316_0,
     author = {Hu, Yao-Zhong},
     title = {Some operator inequalities},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     pages = {316--333},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {28},
     year = {1994},
     mrnumber = {1329122},
     zbl = {0820.47020},
     language = {en},
     url = {http://archive.numdam.org/item/SPS_1994__28__316_0/}
}
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Hu, Yao-Zhong. Some operator inequalities. Séminaire de probabilités de Strasbourg, Tome 28 (1994), pp. 316-333. http://archive.numdam.org/item/SPS_1994__28__316_0/

[1] T. Ando. Topics on Operator Inequalities, mimeographed lecture notes, Hokkaido Univ., Sapporo, 1978. | Zbl

[2] T. Ando. Comparison of the norms ∥f(A)-f(B)∥ and ∥f(|A-B|)∥, Math. Z., 197, 1988, 403-409. | EuDML | MR | Zbl

[3] T. Ando. On some operator inequalities, Math. Ann., 279, 1987, 157-159. | EuDML | MR | Zbl

[4] T. Ando. Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Alg. Appl., 26, 1979, 203-241. | MR | Zbl

[5] H. Araki. On quasi-free states of CAR and Bogoliubov automorphisms, Publ. RIMS Kyoto Univ., 6, 1971, 385-442. | MR | Zbl

[6] H. Araki and S. Yamagami. An inequality for Hilbert-Schmidt norm, Comm. Math. Phys., 81, 1981, 89-96. | MR | Zbl

[7] J. Bendat and S. Sherman. Monotone and convex operator functions, Trans. Amer. Math. Soc., 79, 1955, 58-71. | MR | Zbl

[8] F.A. Berezin. Convex operator functions, Math. Sbornik, 17, 1972, 269-277. | MR | Zbl

[9] R.C. Blei. An elementary proof of the Grothendieck inequality, Proc. Amer. Math. Soc., 100, 1987, 58-60. | MR | Zbl

[10] P.J. Bushell and G.B. Trustrum. Trace inequalities for positive definitive power products, Linear Alg. Appl., 132, 1990, 173-178. | MR | Zbl

[11] M. Breitenecker and H.R. Grümm. Note on trace inequalities, Comm. Math. Phys., 26, 1972, 276-279. | MR | Zbl

[12] K.J. Couteur. Representation of the function Tr(exp(A - λB)) as a Laplace transformation with positive weight and some matrix inequalities, J. Phys. A., 13, 1980, 3147-3149. | MR | Zbl

[13] G. Davis. Notions generalizing convexity for functions defined on space of matrices, Proc. Symposia in Pure Math. : "Convexity", 1963, 159-170. | MR | Zbl

[14] P. Deift. Applications of a commutation formula, Duke Math. J., 45, 1978, 267-310. | MR | Zbl

[15] W. Donoghue. Monotone Matrix Functions and Analytic Continuation, Springer, 1974. | MR | Zbl

[16] H. Epstein. Remarks on two theorems of E. Lieb, Comm. Math. Phys., 31, 1973, 317-325. | MR | Zbl

[17] S. Friedland and M. Katz. On a matrix inequality, Linear Alg. Appl., 85, 1987, 185-190. | MR | Zbl

[18] S. Golden. Lower bounds for the Herglotz functions, Phys. Rev., 137 B, 1965, 1127-1128. | MR | Zbl

[19] A. Grothendieck. Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Mat. Sao Paulo, 8, 1956, 1-79. | MR | Zbl

[20] U. Haagerup. The Grothendieck inequality for the bilinear forms on C* - algebras, Adv. in Math., 56, 1985, 93-116. | MR | Zbl

[21] U. Haagerup. A new upper bound for the complex Grothendieck constant, Israel J. Math., 60, 1987, 199-224. | MR | Zbl

[22] F. Hansen and G.K. Pedersen. Jensen's inequality for operators and Löwner's theorem. Math. Ann., 258, 1982, 229-241. | MR | Zbl

[23] R.A. Horn. The Hadamard product, Proc. Symp. in Applied Math., AMS, 40, 1990, 87-169. | MR | Zbl

[24] Y.Z. Hu. Calculs formels sur les E.D.S. de Stratonovitch, Sém. Prob. 'XXIV,s LNM 1426, Springer, 1990, 453-460. | Numdam | MR | Zbl

[25] J.L. Krivine. Constante de Grothendieck et fonctions de type positif sur les sphères, Adv. Math., 31, 1979, 16-30. | MR | Zbl

[26] A. Korányi. On a theorem of Löwner and its connection with resolvents of selfadjoint transformations, Acta Sci. Math. (Szeged), 17, 1956, 63-70. | MR | Zbl

[27] A. Lenard. Generalization of the Golden-Thompson inequality Tr(eAeB) ≥ Tr(eA+B), Indiana Univ. Math. J., 21, 1971, 457-467. | MR | Zbl

[28] E.H. Lieb. Convex trace functions and the Wigner-Yanase-Dyson conjecture, Adv. in Math., 11, 1973, 267-288. | MR | Zbl

[29] E.H. Lieb and W.E. Thirring. Inequalities for the moments of the eigenvalues of the Schrödinger Hamiltonian and their relation to Sobolev inequalities, Essays in honour of V. Bargman, Princeton, N.J., 1976. | Zbl

[30] K. Löwner. Über monotone Matrixfunctionen, Math. Z., 38, 1934, 117-216. | JFM | Zbl

[31] G. Pisier. Grothendieck's theorem for noncommutative C*-algebras, with an appendix on Grothendieck's constants, J. Funct. Anal., 29, 1978, 397-415. | MR | Zbl

[32] G. Pisier. Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conf. Series in Math., 60, AMS, 1986. | MR | Zbl

[33] R. Reitz. A proof of the Grothendieck inequality, Israel J. Math., 19, 1974, 271-276. | MR | Zbl

[34] M. Rosenblum and J. Rovnyak. Hardy Classes and Operator Theory, Oxford Univ. Press, 1985. | MR | Zbl

[35] B. Simon. Trace Ideals and Their Applications, London Math. Soc. Lect. Notes Series 35, Cambridge Univ. Press, 1979. | MR | Zbl

[36] G. Sparr. A new proof of Löwner's theorem on monotone matrix functions, Math. Scand., 47, 1980, 266-274. | MR | Zbl

[37] B.Sz. Nagy. Remarks on the preceding paper of A. Korányi, Acta Sci. Math. (Szeged) 17, 1956, 71-75. | MR | Zbl

[38] C. Thompson. Inequalities with applications in statistical mechanics, J. Math. Phys., 6, 1965, 1812-1813. | MR

[39] C. Thompson. Inequalities and partial orders on matrix spaces, Indiana Univ. Math. J., 21, 1971, 469-480. | MR | Zbl

The following papers have been known to us after the paper was written. J. Lindenstrauss and A. Pelczynski. Absolutely summing operators in Lp spaces and their applications, Studia Math., 19, 1968, 275-326. | Zbl

K. Ball, E.A. Carlen and E.H. Lieb. Sharp uniform convexity and smoothness inequalities for trace norms, preprint, 1993. | MR

T. Furuta. A proof by operator means of an order preserving inequality. Linear Alg. Appl., 113 :129-130 (1989). | MR | Zbl

M. Fujii, T. Furuta, K. Kamei. Operator functions associated with Furuta's inequality, Linear Alg. Appl., 149 :91-96 (1991). | MR | Zbl

U. Haagerup. Solution of the similarity próblem for cyclic representations of C* - algebras, Ann. of M., 118, 1983, 215-240. | MR | Zbl

U. Haagerup and G. Pisier. Bounded linear operators between C*-algebras, preprint (1993). | MR