Invertibility of nonnegatively Hamiltonian operators in a Hilbert space (Q1603169)

Let \(S,W\) be bounded selfadjoint nonnegative operators in a Hilbert space \(H\) and \(A\) be a closed densely defined operator in \(H\). Under the assumption that the operators \(S\) and \(W\) have bounded inverses or the operator \(A\) has a bounded inverse, bounded invertibility of the operator \[ \begin{pmatrix} A & S\cr W & -A^*\end{pmatrix} \] is proved.