  We prove the statement "The collection of all elements of $\mathcal S$ which
have only simple eigenvalues is dense in $\mathcal S$" for different sets
$\mathcal S$, including: all quantum channels, the unital channels, the
positive trace-preserving maps, all Lindbladians (GKSL-generators), and all
time-dependent Markovian channels. Therefore any element from each of these
sets can always be approximated by diagonalizable elements of the same set to
arbitrary precision.
