Operator inequalities and normal operators (Q437739)

Over the last years, a lot of work has appeared on operator inequalities. The present authors use some advantages offered by the context of finite-dimensional Hilbert spaces and establish complete characterizations of certain distinguished classes of operators (self-adjoint, unitary reflection, normal) in terms of operator inequalities. These results extend the previous characterizations obtained by \textit{A. Seddik} [Linear Multilinear Algebra 59, No. 9, 1069--1074 (2011; Zbl 1222.47057)]. Moreover, the authors extend results of \textit{M. Khosravi} [\textit{M. Khosravi}, Math. Inequal. Appl. 16, No.~2, 477--481 (2013; Zbl 1272.47013)]. Finally, some remarks are made which may stimulate further research.