Characterization of Tracial Functionals by Inequalities for the Spread of a Matrix

Via inequalities for the spread of a matrix we characterize the trace on the full matrix algebra \(\mathbb{M}_{n}(\mathbb{C})\) among all positive linear functionals \(\varphi\) with \(\varphi(I)=n\) , where \(I\) is the unit of \(\mathbb{M}_{n}(\mathbb{C})\) and \(n\geq 3\) . We also present three characterizations of the trace in this class of functionals \(\varphi\) for all \(n\geq 2\) .