Mixed matrix (operator) inequalities Original Research Article

We will show that if 0less-than-or-equals, slantA,B,C and S*S+T*Tless-than-or-equals, slant1, then Aless-than-or-equals, slantS*BS+T*CT implies that image and image These are the extensions of inequalities shown by T. Furuta [Proc. Amer. Math. Soc. 101 (1987) 85; 111 (1991) 511]. Moreover, we will give an inequality, say mixed inequality, which includes the above inequalities and the inequality due to Hansen–Pedersen [Math. Ann. 258 (1982) 229].