Jensen and Minkowski inequalities for operator means and anti-norms

Details Jensen and Minkowski inequalities for operator means and anti-norms Jensen and Minkowski inequalities for operator means and anti-norms

2011-06-11

arxiv.org/abs/1106.2213v3

Mathematics

Functional Analysis

Scientific paper

Jensen inequalities for positive linear maps of Choi and Hansen-Pedersen type are established for a large class of operator/matrix means. These results are also extensions of the Minkowski determinantal inequality. To this end we develop the study of anti-norms, a notion parallel to the symmetric norms in matrix analysis, including functionals like Schatten q-norms for a parameter q<1 and the Minkowski functional. An interpolation theorem for the Schur multiplication is given in this setting. Two sections have been added to the previous version, devoted to means of severable variables and anti-norms.

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