In the theory of semigroups of bounded linear operators ${Z(t)}_{t\geq0}$, the normalized semigroups, $Z(t) : V\rightarrow V$ are defined as follows: $$Z(t)e=e,$$ where $V$ is unital Banach Algebra and 'e' is the multiplicative identity function in $V$.
Now, I am interested to know some of the examples of such normalized linear operators that form a semigroup.