Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A $0-2$ law for cosine families with $\limsup$ to $\infty$   For $\left(C(t)\right)_{t\in\mathbb R}$ being a cosine family on a unital
normed algebra, we show that the estimate $\limsup_{t\to\infty^{+}}\|C(t) - I\|
<2$ implies that $C(t)=I$ for all $t\in\mathbb R$. This generalizes the result
that $\sup_{t\geq0}\|C(t)-I\|<2$ yields that $C(t)=I$ for all $t\geq0$. We also
state the corresponding result for discrete cosine families and for semigroups.

14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat