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- W1536241476 abstract "We prove perturbation theorems for sectoriality and $R$--sectoriality in Banach spaces, which yield results on perturbation of generators of analytic semigroups and on perturbation of maximal $L^p$--regularity. For a given sectorial or $R$--sectorial operator $A$ in a Banach space $X$ we give conditions on intermediate spaces $Z$ and $W$ such that, for an operator $S: Zto W$ of small norm, the perturbed operator $A+S$ is again sectorial or $R$--sectorial, respectively. These conditions are obtained by factorising the perturbation as $S= -BC$, where $B$ acts on an auxiliary Banach space $Y$ and $C$ maps into $Y$. Our results extend previous work on perturbations in the scale of fractional domain spaces associated with $A$ and allow for a greater flexibility in choosing intermediate spaces for the action of perturbation operators. At the end we illustrate our results with several examples, in particular with an application to a ``rough'' boundary-value problem." @default.
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- W1536241476 date "2006-01-01" @default.
- W1536241476 modified "2023-10-13" @default.
- W1536241476 title "Perturbation, interpolation, and maximal regularity" @default.
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- W1536241476 doi "https://doi.org/10.57262/ade/1355867717" @default.
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