  King and Ruskai asked whether the $p\to q$ norm of a completely positive map
$\Phi$, acting between Schatten $p$ and $q$ classes of self-adjoint operators,
$||\Phi||_{p\to q} = \max_{A=A^*} \frac{||\Phi(A)||_q}{||A||_p}$, is equal to
the $p\to q$ norm of that map when acting between Schatten classes of general,
not necessarily self-adjoint, operators. The first proof has been given by
Watrous. We give an alternative proof of this statement.
