The closure of the range of an elementary operator
For a Hilbert space \(H\), consider the operator \(\phi :B(H)\to B(H)\) defined by \(\phi (X)=AXB+CXD\), where \(A\), \(B\), \(C\), and \(D\) are some operators on \(H\). Certain conditions are given which are sufficient for \(B(H)\) to be the topological direct sum of \(\phi^{-1}(0)\) and the range of \(\phi\).
scientific article; zbMATH DE number 2119140
scientific article