On the sum between a closable operator $T$ and a $T$-bounded operator

Abstract

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 Wüst. Our approach involves ranges of matrix operators of the form $\left(\begin{array}{cc}I& A\\ -B& I\end{array}\right)$.