Document Type : Research Paper

Authors

• Leila Nasiri ¹
• Mahmood Shakoori ¹
• Wenshi Liao ²

¹ Department Mathematics, Lorestan University, Iran

² College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, P.R. China

Abstract

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].

Keywords

• Young inequality
• Hilbert-Schmidt norm
• Positive semidefinite matrices
• Refinements