Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Less than one implies zero   In this paper we show that from the estimate $\sup_{t \geq 0}\|C(t) -
\cos(at)I\| <1$ we can conclude that $C(t)$ equals $\cos(at) I$. Here
$\left(C(t)\right)_{t \geq 0}$ is a strongly continuous cosine family on a
Banach space.

21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess