Abstract

In this paper, we give some Young type inequalities for scalars. By using these inequalities we establish corresponding Young type inequalities for matrices. In addition, we present some reverses of the Young type inequalities and give several refinements for matrices.

Keywords: Heinz mean inequalities; positive semidefinite matrices; Hilbert-Schmidt norm; Young inequality.

MSC: 26D07, 26D15, 15A18, 47A63

Pages:  163$-$173     

Volume  74 ,  Issue  3 ,  2022