Square Root Problem of Kato for the Sum of Operators

This paper is concerned with the square root problem of Kato for the “sum” of linear operators in a Hilbert space $\mathbb{H}$. Under suitable assumptions, we show that if $A$ and $B$ are respectively m-scetroial linear operators satisfying the square root problem of Kato. Then the same conclusion still holds for their “sum”. As application, we consider perturbed Schr"{o}dinger operators.