Let $\displaystyle {T}_{n}\to T$, where $\displaystyle {T}_{n}\in B(X,Y).$. show that for every $\displaystyle \epsilon > 0$ and every closed ball $\displaystyle K\subset X$ there is an N such that [tex] $\displaystyle \left\|T_nx-Tx\right\| < \epsilon $ for all n > N and $\displaystyle x\in K$