Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Eventual Regularity Properties of Operator-Valued Functions   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
$t\mapsto u(t)x$ has a regularity property (e.g. continuity, differentiability,
etc.) on some interval $(t_x,\infty)$ in general depending on $x\in X$. 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.

3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess