Functional analysis convergence question

[iceblue]

If X is Banach space and F:X \rightarrow X is a linear and bounded map and that F^n(x)\rightarrow0 pointwise .. How can I show that it converges to zero uniformly also?

Thanks

 

[Eynstone]

http: //en.wikipedia.org/wiki/Bounded_operator#Equivalence_of_boundedness_and_continuity