A relation between completely bounded norms and conjugate channels
  We show a relation between a quantum channel $\Phi$ and its conjugate $\Phi^C$, which implies that the $p\to p$ Schatten norm of the channel is the same as the $1\to p$ completely bounded norm of the conjugate. This relation is used to give an alternative proof of the multiplicativity of both norms. 
Anna Jencova