Operator-Theoretic Methods for Matrix Inequalities

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1 The Golden-thompson inequality concerning exponential functions for a pair of matrices is generalized to the case of more than three matrices by using Hadamard products.[Reference 1]2 Performing inverse operations before and after a positive linear map produces stronger order relation. The fundamental structure of this strong order is analyzed.[Reference 2]3 A reasonable upper bound is given for the farthest distance from one normal matrix to the set of unitary orbits of the other normal matrix.[Reference 3]4 Besides the usual norms, a family of operator radii omega_<rho>(・)(0<rho<*) is considered in the space of matrices. An interpolation theorem, in the form of Holder type inequality, is established for this family of operator radii with respect to Hadamard multiplication. [Reference 4, 5]5 A way of generalizing the Holder type inequality to the matrix case is investigated. They are established in the form of matrix inequality as well as in the trace inequality. [Reference 6]A survey article with title Operator-Theoretic Methods for Matrix Inequalities is prepared to let the results widely be recognized by researchers in the world.