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Log majorization and complementary Golden-Thompson type inequalities. (English) Zbl 0793.15011

The authors obtain a log majorization result for power means of positive semidefinite matrices. Logarithmic trace inequalities and determinant inequalities are reduced as applications of their results.

MSC:

15A45 Miscellaneous inequalities involving matrices
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
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[1] Ando, T., Majorization, doubly stochastic matrices, and comparison of eigenvalues, Linear Algebra Appl., 118, 163-248 (1989) · Zbl 0673.15011
[2] Araki, H., On an inequality of Lieb and Thirring, Lett. Math. Phys., 19, 167-170 (1990) · Zbl 0705.47020
[3] Bernstein, D. S., Inequalities for the trace of matrix exponentials, SIAM J. Matrix Anal. Appl., 9, 156-158 (1988) · Zbl 0658.15018
[4] Cohen, J. E., Spectral inequalities for matrix exponentials, Linear Algebra Appl., 111, 25-28 (1988) · Zbl 0662.15012
[5] Bhatia, R., Perturbation Bounds for Matrix Eigenvalues, (Pitman Res. Notes Math. Ser. 162 (1987), Longman) · Zbl 0696.15013
[6] Furuta, T., \(A⩾B⩾0 assures ( B^r A^p B^r )^{1q} ⩾B^{(p+2r)q}\) for \(r\)⩾\(0, p>0, q\)⩾1 with \((1+2r)q\)⩾\(p+2r\), Proc. Amer. Math. Soc., 101, 85-88 (1987) · Zbl 0721.47023
[7] Golden, S., Lower bounds for Helmholtz function, Phys. Rev., 137, B1127-B1128 (1965) · Zbl 0125.23204
[8] Hiai, F.; Petz, D., The Golden-Thompson trace inequality is complemented, Linear Algebra Appl., 181, 153-185 (1993) · Zbl 0784.15011
[9] Kubo, F.; Ando, T., Means of positive linear operators, Math. Ann., 246, 205-224 (1980) · Zbl 0412.47013
[10] Lenard, A., Generalization of the Golden-Thompson inequality Tr(\(e^A e^B\))⩾Tr\(e^{A+B} \), Indiana Univ. Math. J., 21, 457-467 (1971) · Zbl 0215.08606
[11] Marshall, A. W.; Olkin, I., Inequalities: Theory of Majorization and its Applications (1979), Academic: Academic New York · Zbl 0437.26007
[12] Reed, M.; Simon, B., Methods of Modern Mathematical Physics I: Functional Analysis (1980), Academic: Academic New York, (revised and enlarged ed.)
[13] Thompson, C. J., Inequality with applications in statistical mechanics, J. Math. Phys., 6, 1812-1813 (1965)
[14] Thompson, C. J., Inequalitied and partial orders on matrix spaces, Indiana Univ. Math. J., 21, 469-480 (1971) · Zbl 0227.15005
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