A cheap way to closed operator sums
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912786383110144 |
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| author | Haak, Bernhard H. Kunstmann, Peer Christian |
| author_facet | Haak, Bernhard H. Kunstmann, Peer Christian |
| contents | Let $A$ and $B$ be sectorial operators in a Banach space $X$ of angles $ω_A$ and $ω_B$, respectively, where $ω_A+ω_B<π$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A cheap way to closed operator sums Haak, Bernhard H. Kunstmann, Peer Christian Functional Analysis Analysis of PDEs 47A60 47D06 Let $A$ and $B$ be sectorial operators in a Banach space $X$ of angles $ω_A$ and $ω_B$, respectively, where $ω_A+ω_B<π$. 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. |
| title | A cheap way to closed operator sums |
| topic | Functional Analysis Analysis of PDEs 47A60 47D06 |
| url | https://arxiv.org/abs/2512.15594 |