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- W4287575211 abstract "Let $mathcal{L}(X;Y)$ be the space of bounded linear operators from a Banach space $X$ to a Banach space $Y$. Given an operator-valued function $u:mathbb{R}_{geq 0}rightarrow mathcal{L}(X;Y)$, suppose that every orbit $tmapsto u(t)x$ has a regularity property (e.g. continuity, differentiability, etc.) on some interval $(t_x,infty)$ in general depending on $xin X$. In this paper we develop an abstract set-up based on Baire-type arguments which allows, under certain conditions, removing the dependency on $x$ systematically. Afterwards, we apply this theoretical framework to several different regularity properties that are of interest also in semigroup theory. In particular, a generalisation of the prior results on eventual differentiability of strongly continuous functions $u:mathbb{R}_{geq 0} rightarrow mathcal{L}(X;Y)$ obtained by Iley and B'arta follows as a special case of our method." @default.
- W4287575211 created "2022-07-25" @default.
- W4287575211 creator A5053605280 @default.
- W4287575211 date "2020-12-01" @default.
- W4287575211 modified "2023-09-26" @default.
- W4287575211 title "On Eventual Regularity Properties of Operator-Valued Functions" @default.
- W4287575211 doi "https://doi.org/10.48550/arxiv.2012.00615" @default.
- W4287575211 hasPublicationYear "2020" @default.
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