Possible Duplicate:
Do continuous linear functions between Banach spaces extend?
Is there an example of a pair of Banach spaces $X$ and $Y$, a subspace $E\subseteq X$ and a bounded linear operator $T:E\rightarrow Y$ (with the norm on $E$ induced by the norm on $X$) such that there doesn't exist an extension $\hat T:X\rightarrow Y$ of $T$?
