AN OPERATOR alpha -GEOMETRIC MEAN INEQUALITY

作者：Fu, Xiaohui^*

来源：Journal of Mathematical Inequalities, 2015, 9(3): 947-950.

DOI：10.7153/jmi-09-77

• Operator inequality
• alpha -geometric mean
• positive linear map

We square operator alpha -geometric mean inequality as follows: If 0 < m(1) <= A <= M-1 and 0 < m(2) <= B <= M-2 for some positive real numbers m(1) < M-1 and m(2) < M-2, then for every unital positive linear map Phi and alpha epsilon [0,1], the following inequality holds: @@@ (Phi(A)#(alpha)Phi(B))(2) <= ((M-1 + m(1))(2)((M-1 + m(1))(-1)(M-2 + m(2)))(2 alpha)/4(m(2)M(2))(alpha)(m(1)M(1))((1-alpha)))(2) Phi(2)(A#B-alpha).

• 出版日期2015-9
• 单位海南师范大学