On generalized Powers-St$\o$rmer's Inequality
  A generalization of Powers-St$\o$rmer's inequality for operator monotone functions on $[0, +\infty)$ and for positive linear functional on general $C^*$-algebras will be proved. It also will be shown that the generalized Powers-St$\o$rmer inequality characterizes the tracial functionals on $C^*$-algebras. 
Dinh Trung Hoa, Hiroyuki Osaka, Ho Minh Toan
math.OA