In my research of operator algebras and their connection with machine learning I of course use the well know result:
For the map $ tr:M_n \to M_n $ denoting the transpose map of matrices (meaning that $ tr(A)=A^{tr} $ we know for the completely bounded norm (cb-norm) that $ ||tr||_{cb}=n $
I keep using this result freely but to be honest it had just occurred to me that I know not a proof of this nor do I have a reference for the proof or an idea for proving it that would actually work, could operator algebraists out there please help in providing a proof or a reference to a nice (or any...) functioning proof of this useful fact?