We introduce the super-shadowing property in linear dynamics, where pseudotrajectories are approximated by sequences of the form \((\lambda _n T^n x)\) , with \((\lambda _n)_n\) being complex scalars. For compact operators on Banach spaces, we characterize the operators that possess the positive super-shadowing property and the positive limit super-shadowing property. Additionally, we demonstrate that no surjective isometric operator on a separable Banach space \(X\) with \(\text {dim}(X)>1\) can exhibit the positive super-shadowing property. Finally, we provide some results on upper frequently supercyclic and reiteratively supercyclic operators.
