Young and Inverse Young Inequalities on Euclidean Jordan Algebra

This paper is mainly to do in-depth research on inequalities on symmetric cones. We will conduct further analysis and discussion based on the inequalities we have developed on the second-order cone, and develop more inequalities. According to our past research in dealing with second-order cone inequalities, we derive more inequalities concerning eigenvalue version of Young inequality and trace version of inverse Young inequality. These results coincide with the conclusions on the positive semidefinite cone, which is also a symmetric cone. It is of considerable help to the establishment of inequalities on symmetric cones and the analysis of their derivative algorithms.