Some versions of Anderson's and Maher's inequalities. I (Q1415184)

In this paper, firstly, the author discusses equivalence conditions for when the inequality \( \| T+\Delta_{A,B}(X)\| _{p}\geq \| T\| _{p}\) holds, where \(\Delta_{A,B}(X)=AXB-X\) and \(\| \cdot\| _{p}\) means the Schatten \(p\)-norm. As generalizations of these results, the author discusses equivalence relations for when the following norm inequality holds: \( \| T+E_{A,B}(X)\| _{p}\geq \| T\| _{p}\), where \(E_{A,B}(X)=\sum_{i=1}^{n}A_{i}XB_{i}-X\). Next, the author discusses equality conditions for the above inequalities and obtains related results.