A Note on Indefinite Chaotic Order - Bebiano, N.
A selfadjoint involutive matrix J endows C^n with an indefinite inner product [¢; ¢] defined by [x,y]:= y*Jx, x,y \in C^n. For a pair of J-selfadjoint matrices A, B with positive eigenvalues, LogA ≥_J LogB is called the J-chaotic order or indefinite chaotic order. In this note a characterization of the indefinite chaotic order in terms of the alpha-power mean is revisited and a related open problem is proposed. A new characterization of the indefinite chaotic order is also obtained.