Operator inequalities related to weak 2-positivity
  In this paper we introduce the notion of weak 2-positivity and present some examples. We establish some operator Cauchy--Schwarz inequalities involving the geometric mean and give some applications. In particular, we present some operator versions of Hua's inequality by using the Choi--Davis--Jensen inequality. 
Mohammad Sal Moslehian and Jun Ichi Fujii
math.FA math.OA