@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://www.numdam.org/item/SPS_1994__28__316_0/} }
Hu, Yao-Zhong. Some operator inequalities. Séminaire de probabilités de Strasbourg, Tome 28 (1994), pp. 316-333. http://www.numdam.org/item/SPS_1994__28__316_0/
[1] Topics on Operator Inequalities, mimeographed lecture notes, Hokkaido Univ., Sapporo, 1978. | Zbl
.[2] Comparison of the norms ∥f(A)-f(B)∥ and ∥f(|A-B|)∥, Math. Z., 197, 1988, 403-409. | EuDML | MR | Zbl
.[3] On some operator inequalities, Math. Ann., 279, 1987, 157-159. | EuDML | MR | Zbl
.[4] Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Alg. Appl., 26, 1979, 203-241. | MR | Zbl
.[5] On quasi-free states of CAR and Bogoliubov automorphisms, Publ. RIMS Kyoto Univ., 6, 1971, 385-442. | MR | Zbl
.[6] An inequality for Hilbert-Schmidt norm, Comm. Math. Phys., 81, 1981, 89-96. | MR | Zbl
and .[7] Monotone and convex operator functions, Trans. Amer. Math. Soc., 79, 1955, 58-71. | MR | Zbl
and .[8] Convex operator functions, Math. Sbornik, 17, 1972, 269-277. | MR | Zbl
.[9] An elementary proof of the Grothendieck inequality, Proc. Amer. Math. Soc., 100, 1987, 58-60. | MR | Zbl
.[10] Trace inequalities for positive definitive power products, Linear Alg. Appl., 132, 1990, 173-178. | MR | Zbl
and .[11] Note on trace inequalities, Comm. Math. Phys., 26, 1972, 276-279. | MR | Zbl
and .[12] 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] Notions generalizing convexity for functions defined on space of matrices, Proc. Symposia in Pure Math. : "Convexity", 1963, 159-170. | MR | Zbl
.[14] Applications of a commutation formula, Duke Math. J., 45, 1978, 267-310. | MR | Zbl
.[15] Monotone Matrix Functions and Analytic Continuation, Springer, 1974. | MR | Zbl
.[16] Remarks on two theorems of E. Lieb, Comm. Math. Phys., 31, 1973, 317-325. | MR | Zbl
.[17] On a matrix inequality, Linear Alg. Appl., 85, 1987, 185-190. | MR | Zbl
and .[18] Lower bounds for the Herglotz functions, Phys. Rev., 137 B, 1965, 1127-1128. | MR | Zbl
.[19] Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Mat. Sao Paulo, 8, 1956, 1-79. | MR | Zbl
.[20] The Grothendieck inequality for the bilinear forms on C* - algebras, Adv. in Math., 56, 1985, 93-116. | MR | Zbl
.[21] A new upper bound for the complex Grothendieck constant, Israel J. Math., 60, 1987, 199-224. | MR | Zbl
.[22] Jensen's inequality for operators and Löwner's theorem. Math. Ann., 258, 1982, 229-241. | MR | Zbl
and .[23] The Hadamard product, Proc. Symp. in Applied Math., AMS, 40, 1990, 87-169. | MR | Zbl
.[24] Calculs formels sur les E.D.S. de Stratonovitch, Sém. Prob. 'XXIV,s LNM 1426, Springer, 1990, 453-460. | Numdam | MR | Zbl
.[25] Constante de Grothendieck et fonctions de type positif sur les sphères, Adv. Math., 31, 1979, 16-30. | MR | Zbl
.[26] On a theorem of Löwner and its connection with resolvents of selfadjoint transformations, Acta Sci. Math. (Szeged), 17, 1956, 63-70. | MR | Zbl
.[27] Generalization of the Golden-Thompson inequality Tr(eAeB) ≥ Tr(eA+B), Indiana Univ. Math. J., 21, 1971, 457-467. | MR | Zbl
.[28] Convex trace functions and the Wigner-Yanase-Dyson conjecture, Adv. in Math., 11, 1973, 267-288. | MR | Zbl
.[29] 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
and .[30] Über monotone Matrixfunctionen, Math. Z., 38, 1934, 117-216. | JFM | Zbl
.[31] Grothendieck's theorem for noncommutative C*-algebras, with an appendix on Grothendieck's constants, J. Funct. Anal., 29, 1978, 397-415. | MR | Zbl
.[32] Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conf. Series in Math., 60, AMS, 1986. | MR | Zbl
.[33] A proof of the Grothendieck inequality, Israel J. Math., 19, 1974, 271-276. | MR | Zbl
.[34] Hardy Classes and Operator Theory, Oxford Univ. Press, 1985. | MR | Zbl
and .[35] Trace Ideals and Their Applications, London Math. Soc. Lect. Notes Series 35, Cambridge Univ. Press, 1979. | MR | Zbl
.[36] A new proof of Löwner's theorem on monotone matrix functions, Math. Scand., 47, 1980, 266-274. | MR | Zbl
.[37] Remarks on the preceding paper of A. Korányi, Acta Sci. Math. (Szeged) 17, 1956, 71-75. | MR | Zbl
.[38] Inequalities with applications in statistical mechanics, J. Math. Phys., 6, 1965, 1812-1813. | MR
.[39] 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. Absolutely summing operators in Lp spaces and their applications, Studia Math., 19, 1968, 275-326. | Zbl
and .Sharp uniform convexity and smoothness inequalities for trace norms, preprint, 1993. | MR
, and .A proof by operator means of an order preserving inequality. Linear Alg. Appl., 113 :129-130 (1989). | MR | Zbl
.Operator functions associated with Furuta's inequality, Linear Alg. Appl., 149 :91-96 (1991). | MR | Zbl
, , .Solution of the similarity próblem for cyclic representations of C* - algebras, Ann. of M., 118, 1983, 215-240. | MR | Zbl
.Bounded linear operators between C*-algebras, preprint (1993). | MR
and .