  We give a sufficient condition for the sum of two closed operators to be
closed. In particular, we study the sum of two sectorial operators with the sum
of their sectoriality angles greater than $\pi$. We show that if one of the
operators admits bounded $H^{\infty}$-calculus and the resolvent of the other
operator satisfies a boundedness condition stronger than the standard
sectoriality, but weaker than the bounded imaginary powers property in the case
of UMD spaces, then the sum is closed. We apply the result to the abstract
parabolic problem and give a sufficient condition for $L^{p}$-maximal
regularity.
