In the present paper, taking some advantages offered by the context of finite dimensional Hilbert spaces, we shall give a complete characterizations of certain distinguished classes of operators (self-adjoint, unitary reflection, normal) in terms of operator inequalities. These results extend previous characterizations obtained by the second author.
"Operator inequalities and normal operators." Banach J. Math. Anal. 6 (2) 204 - 210, 2012. https://doi.org/10.15352/bjma/1342210170