Some operator inequalities

 Access to full text

 Full (PDF)

1. [1] T. Ando. Topics on Operator Inequalities, mimeographed lecture notes, Hokkaido Univ., Sapporo, 1978. Zbl0388.47024
2. [2] T. Ando. Comparison of the norms ∥f(A)-f(B)∥ and ∥f(|A-B|)∥, Math. Z., 197, 1988, 403-409. Zbl0618.47007MR926848
3. [3] T. Ando. On some operator inequalities, Math. Ann., 279, 1987, 157-159. Zbl0613.47020MR912844
4. [4] T. Ando. Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Alg. Appl., 26, 1979, 203-241. Zbl0495.15018MR535686
5. [5] H. Araki. On quasi-free states of CAR and Bogoliubov automorphisms, Publ. RIMS Kyoto Univ., 6, 1971, 385-442. Zbl0227.46061MR295702
6. [6] H. Araki and S. Yamagami. An inequality for Hilbert-Schmidt norm, Comm. Math. Phys., 81, 1981, 89-96. Zbl0468.47013MR630332
7. [7] J. Bendat and S. Sherman. Monotone and convex operator functions, Trans. Amer. Math. Soc., 79, 1955, 58-71. Zbl0064.36901MR82655
8. [8] F.A. Berezin. Convex operator functions, Math. Sbornik, 17, 1972, 269-277. Zbl0279.47006MR300121
9. [9] R.C. Blei. An elementary proof of the Grothendieck inequality, Proc. Amer. Math. Soc., 100, 1987, 58-60. Zbl0637.46017MR883401
10. [10] P.J. Bushell and G.B. Trustrum. Trace inequalities for positive definitive power products, Linear Alg. Appl., 132, 1990, 173-178. Zbl0701.15015MR1058100
11. [11] M. Breitenecker and H.R. Grümm. Note on trace inequalities, Comm. Math. Phys., 26, 1972, 276-279. Zbl0254.47036MR312309
12. [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. Zbl0446.44002MR587741
13. [13] G. Davis. Notions generalizing convexity for functions defined on space of matrices, Proc. Symposia in Pure Math. : "Convexity", 1963, 159-170. Zbl0196.30303MR155837
14. [14] P. Deift. Applications of a commutation formula, Duke Math. J., 45, 1978, 267-310. Zbl0392.47013MR495676
15. [15] W. Donoghue. Monotone Matrix Functions and Analytic Continuation, Springer, 1974. Zbl0278.30004MR486556
16. [16] H. Epstein. Remarks on two theorems of E. Lieb, Comm. Math. Phys., 31, 1973, 317-325. Zbl0257.46089MR343073
17. [17] S. Friedland and M. Katz. On a matrix inequality, Linear Alg. Appl., 85, 1987, 185-190. Zbl0612.15010MR869352
18. [18] S. Golden. Lower bounds for the Herglotz functions, Phys. Rev., 137 B, 1965, 1127-1128. Zbl0125.23204MR189691
19. [19] A. Grothendieck. Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Mat. Sao Paulo, 8, 1956, 1-79. Zbl0074.32303MR94682
20. [20] U. Haagerup. The Grothendieck inequality for the bilinear forms on C* - algebras, Adv. in Math., 56, 1985, 93-116. Zbl0593.46052MR788936
21. [21] U. Haagerup. A new upper bound for the complex Grothendieck constant, Israel J. Math., 60, 1987, 199-224. Zbl0646.46019MR931877
22. [22] F. Hansen and G.K. Pedersen. Jensen's inequality for operators and Löwner's theorem. Math. Ann., 258, 1982, 229-241. Zbl0473.47011MR649196
23. [23] R.A. Horn. The Hadamard product, Proc. Symp. in Applied Math., AMS, 40, 1990, 87-169. Zbl0712.15011MR1059485
24. [24] Y.Z. Hu. Calculs formels sur les E.D.S. de Stratonovitch, Sém. Prob. 'XXIV,s LNM1426, Springer, 1990, 453-460. Zbl0702.60055MR1071561
25. [25] J.L. Krivine. Constante de Grothendieck et fonctions de type positif sur les sphères, Adv. Math., 31, 1979, 16-30. Zbl0413.46054MR521464
26. [26] A. Korányi. On a theorem of Löwner and its connection with resolvents of selfadjoint transformations, Acta Sci. Math. (Szeged), 17, 1956, 63-70. Zbl0074.10202MR82656
27. [27] A. Lenard. Generalization of the Golden-Thompson inequality Tr(eAeB) ≥ Tr(eA+B), Indiana Univ. Math. J., 21, 1971, 457-467. Zbl0215.08606MR289536
28. [28] E.H. Lieb. Convex trace functions and the Wigner-Yanase-Dyson conjecture, Adv. in Math., 11, 1973, 267-288. Zbl0267.46055MR332080
29. [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. Zbl0342.35044
30. [30] K. Löwner. Über monotone Matrixfunctionen, Math. Z., 38, 1934, 117-216. Zbl0008.11301JFM60.0055.01
31. [31] G. Pisier. Grothendieck's theorem for noncommutative C*-algebras, with an appendix on Grothendieck's constants, J. Funct. Anal., 29, 1978, 397-415. Zbl0388.46043MR512252
32. [32] G. Pisier. Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conf. Series in Math., 60, AMS, 1986. Zbl0588.46010MR829919
33. [33] R. Reitz. A proof of the Grothendieck inequality, Israel J. Math., 19, 1974, 271-276. Zbl0321.46018MR367628
34. [34] M. Rosenblum and J. Rovnyak. Hardy Classes and Operator Theory, Oxford Univ. Press, 1985. Zbl0586.47020MR822228
35. [35] B. Simon. Trace Ideals and Their Applications, London Math. Soc. Lect. Notes Series 35, Cambridge Univ. Press, 1979. Zbl0423.47001MR541149
36. [36] G. Sparr. A new proof of Löwner's theorem on monotone matrix functions, Math. Scand., 47, 1980, 266-274. Zbl0433.15012MR612700
37. [37] B.Sz. Nagy. Remarks on the preceding paper of A. Korányi, Acta Sci. Math. (Szeged)17, 1956, 71-75. Zbl0074.10203MR82657
38. [38] C. Thompson. Inequalities with applications in statistical mechanics, J. Math. Phys., 6, 1965, 1812-1813. MR189688
39. [39] C. Thompson. Inequalities and partial orders on matrix spaces, Indiana Univ. Math. J., 21, 1971, 469-480. Zbl0227.15005MR294372
40. 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. Zbl0183.40501
41. K. Ball, E.A. Carlen and E.H. Lieb. Sharp uniform convexity and smoothness inequalities for trace norms, preprint, 1993. Zbl0803.47037MR1262940
42. T. Furuta. A proof by operator means of an order preserving inequality. Linear Alg. Appl., 113 :129-130 (1989). Zbl0770.47003MR978587
43. M. Fujii, T. Furuta, K. Kamei. Operator functions associated with Furuta's inequality, Linear Alg. Appl., 149 :91-96 (1991). Zbl0725.47023MR1092871
44. U. Haagerup. Solution of the similarity próblem for cyclic representations of C* - algebras, Ann. of M., 118, 1983, 215-240. Zbl0543.46033MR717823
45. U. Haagerup and G. Pisier. Bounded linear operators between C*-algebras, preprint (1993). Zbl0803.46064MR1240608