Let $X$ be a Banach space. Can I have an example of a strongly continuous group of operators $T(t)$ such that $$|T(t)x|\geq c |x|, \ t\in\mathbb{R}$$with $c>1$.
For $c=1$, I know examples of groups of isometries. In general we have this estimation $$|T(t)x|\leq Me^{\omega |t|} |x|, \ t\in\mathbb{R}.$$