在序A^4≥(A^2B^2A^2)^(2/3)下的α幂平均函数的单调性

Monotonicity of Some α-Power Mean Functions under the Order Defined by A^4≥(A^2B^2A^2)^(2/3)

讨论了Hilbert空间H上两严格正算子A,B的一种比A2≥AB2A1/2更弱的序关系A4≥A2B2A22/3,并且讨论了在这种序关系下若干α幂平均函数的算子单调性.

An order A^4≥（A^2B^2A^2）^2/3 between any two strictly positive operators A and B on a Hilbert 1 space H is discussed, which is weaker than A^2≥ （AB^2A）^1/2. The operator monotonicity of α - power mean functions associated with this order is shown.