  King and Ruskai asked whether the norm of a completely positive map acting
between Schatten classes of operators is equal to that of its restriction to
the real subspace of self-adjoint operators. Proofs have been promptly supplied
by Watrous and Audenaert. Here we provide one more proof, in fact of a slightly
more general fact, under the (slightly weaker) assumption of 2-positivity. The
argument is elementary and self-contained.
