  A proof using the theory of completely positive maps is given to the fact
that if $A \in M_2$, or $A \in M_3$ has a reducing eigenvalue, then every
bounded linear operator $B$ with $W(B) \subseteq W(A)$ has a dilation of the
form $I \otimes A$. This gives a unified treatment for the different cases of
the result obtained by researchers using different techniques.
