How to realize the multiplication of a optimization variable in CVX? Or is there another way(not restricted to CVX) to realize it?

it appears that the argument of the norm is a matrix (even though there appears to be a typo in the dimensions you provided for A and `X). Therefore, that is the operator two-norm, i.e., the largest singular value of the matrix argument. If that argument is not affine, which it isn’t here. I don’t believe that will be convex.