Reverse inequality to Golden–Thompson type inequalities: Comparison of eA+B and eAeB Original Research Article

Let A and B be n-by-n Hermitian matrices. Thenimagewhere α is the condition number of eA and S(t) is the Specht ratio of the reverse arithmetic-geometric mean inequality. It is a sharp reverse result to the Golden–Thompson inequality. This can be extended to each eigenvalue. Equivalently there exists a unitary V such thateA/2eBeA/2less-than-or-equals, slantS(α)VeA+BV*.We also show that there exists a unitary W such thatWeA+BW*less-than-or-equals, slantS(α)eA/2eBeA/2.