Example of operator with $\lVert T \rVert^ i = 1$ in normed spaces

Question

Let X be a normed vector space of your choice with its norm $\lVert.\rVert$. I am looking for an operator of norm $\lVert T \rVert ^ i = 1$.

Defined on as $T:X \rightarrow X$ s.t. its powers $T^{i} = T \circ T^{i-1}$ for all $i \geq 1$.

Here is where I am having trouble though, it needs to have $T^{i} \neq T^{i-1}$

Any thoughts would be much appreciated.