On the sum between a closable operator $T$ and a $T$-bounded operator
  We provide several perturbation theorems regarding closable operators on a real or complex Hilbert space. In particular we extend some classical results due to Hess--Kato, Kato--Rellich and W\"ust. Our approach involves ranges of matrix operators of the form $\left(\begin{array}{cc}\!\! I & A\!\!\\ \!\! -B& I\!\!\end{array}\right)$. 
Dan Popovici, Zolt\'an Sebesty\'en, Zsigmond Tarcsay
math.FA