AN ORDER PRESERVING INEQUALITY FOR THREE OPERATORS VIA FURUTA INEQUALITY

作者：Yang Changsen^*

来源：Acta Mathematica Scientia, 2008, 28(4): 998-1002.

• Positive operator
• Furuta inequality
• operator inequality

Furuta showed that if A >= B >= 0, then for each r >= 0, f(p) = (A(r/2)B(p)A(r/2))(t+r/p+r) is decreasing for p >= t >= 0. Using this result, the following inequality (C(r/2)(AB(2)A)(delta)C(r/2))(p-1+r/4 delta+r) <= C(p-1+r) is obtained for 0 < p <= 1, r >= 1, 1/4 <= delta <= 1 and three positive operators, A, B, C satisfy (A(1/2)BA(1/2))(p/2) <= A(p), (B(1/2)AB(1/2))(p/2) >= B(p), (C(1/2)AC(1/2))(p/2) <= C(p), (A(1/2)CA(1/2))(p/2) >= A(p).

• 出版日期2008-10
• 单位河南师范大学