Norm equality for a basic elementary operator. (Q1413186)

Let \(\mathcal{L}(H)\) be the algebra of bounded linear operators on a Hilbert space \(H\). For \(A\), \(B\in\mathcal{L}(H)\), define the elementary operator \(M_{A,B}\) by \(M_{A,B}(X)=AXB\) \((X\in\mathcal{L}(H))\). The authors give necessary and sufficient conditions for any pair of operators \(A\) and \(B\) to satisfy the equation \(\| I+M_{A,B}\| =1+\| A\| \| B\| \).