A cheap way to closed operator sums

Bernhard H. Haak; Peer Christian Kunstmann

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arXiv · 2512.15594

A cheap way to closed operator sums

Bernhard H. Haak·Peer Christian Kunstmann

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Abstract

Let $A$ and $B$ be sectorial operators in a Banach space $X$ of angles $\omega_A$ and $\omega_B$, respectively, where $\omega_A+\omega_B<\pi$. 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 $\ell^q$-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.

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BibTeX RIS

Bernhard H. Haak, Peer Christian Kunstmann. 2025-12-17. A cheap way to closed operator sums. https://arxiv.org/abs/2512.15594

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