Less than one implies zero
Volume 229 / 2015
Studia Mathematica 229 (2015), 181-188
MSC: Primary 47D09; Secondary 47D06.
DOI: 10.4064/sm8218-12-2015
Published online: 16 December 2015
Abstract
In this paper we show that from an estimate of the form $\sup_{t \geq 0}\| C(t) - \cos(at)I\| <1$, we can conclude that $C(t)$ equals $\cos(at) I$. Here $(C(t))_{t \geq 0}$ is a strongly continuous cosine family on a Banach space.
