Accretive operators and Cassels inequality
Based on the notion of accretive operator, the author presents a method of extending the range of applicability of some matrix inequalities. He extends some inequalities from positive definite matrices to the case of matrices \(Z\) having an accretive transform \((Z-mI)^{\ast }(MI-Z)\). One of the results is the following: Let \(A,Z\in M_{n}(R)\) with \(A\geq 0\) and let scalars \(m,M\) be positive such that \(\text{Re}\langle h,(Z-mI)^{\ast }(MI-Z)h\rangle \geq 0\) for all \(h\in R^n\). Then \[ Tr~|AZ| \leq \frac{M+m}{2\sqrt{Mm}}Tr~AZ, \] where \(|U|=(U^{\ast }U)^{1/2}\).
scientific article; zbMATH DE number 5710779