A Characterization of the Operator Entropy in terms of an Isometry Property Related to Trace Norms

In this paper, we introduce two new mean operators acting on trace class operators, and using the mean operators, we provide a new characterization theorem of operator entropy in terms of an isometry property between two trace norms. It is a very important point that we can characterize the operator entropy only using the isometry property for a continuous operator on some class of density operators.