A cheap way to closed operator sums

Bernhard H. Haak; Peer Christian Kunstmann

paper

A cheap way to closed operator sums

arXiv:2512.15594

Abstract

Let $A$ and $B$ be sectorial operators in a Banach space $X$ of angles $I ¨ _{A}$ and $I ¨ _{B}$ , respectively, where $I ¨ _{A} + I ¨ _{B} < I ¨ $ . We present a simple and common approach to results on closedness of the operator sum $A + B$ , based on Littlewood-Paley type norms and tools from several interpolation theories. This allows us to give short proofs for the well-known results due to Da~Prato-Grisvard and Kalton-Weis. We prove a new result in $ℓ^{q}$ -interpolation spaces and illustrate it with a maximal regularity result for abstract parabolic equations. Our approach also yields a new proof for the Dore-Venni result.

26 pages