Document Type : Research Paper
Department Mathematics, Lorestan University, Iran
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. China
In this paper, we present some refinements of the famous Young type inequality. As application of our result, we obtain some matrix inequalities for the Hilbert-Schmidt norm and the trace norm. The results obtained in this paper can be viewed as refinement of the derived results by H. Kai [Young type inequalities for matrices, J. East China Norm. Univ. 4 (2012) 12--17].