Hi I just dont know if this proposition is true, I think it is but I dont know how to start:
Let $X$ be a Banach space of infinite dimension, if $T \in B(x)$ and there is an $N$ such that $T^N=I$ then T is not compact.
I clearly know that $T^N$ is not compact but does that implie that $T$ isnt?
thx for your help