SOME GENERALIZATIONS OF OPERATOR INEQUALITIES

作者：Fu, Xiaohui^*

来源：Journal of Mathematical Inequalities, 2015, 9(1): 101-105.

DOI：10.7153/jmi-09-09

• Operator inequalities
• positive linear maps
• arithmetic mean
• geometric mean

In this paper, we generalize some operator inequalities as follows: Let A, A(i) (i = 1,...,n) be positive operators on a Hilbert space with 0 < m <= A, A(i) <= M ( i = 1,...,n). Then for 1 <= p < infinity and every positive unital linear map Phi, @@@ Phi(p)(A(-1)) Phi(p)(A) + Phi(p)(A) Phi(p)(A(-1)) <= (M + m)(2p)/2M(p)m(p), @@@ and @@@ [GRAPHICS] @@@ where G(A(1),...,A(n)) is Ando-Li-Mathias geometric mean [1].

• 出版日期2015-3
• 单位海南师范大学