Classical computational spectral problem

The classical computational spectral problem takes $\Omega =\mathcal{B}({\ell }^2(\mathbb{N}))$, reads the matrix entries $⟨A{e}_j,e_i⟩$, and asks for $\mathrm{Sp}(A)$ in the Hausdorff distance or Attouch--Wets topology. Its Solvability complexity index is three for general bounded operators.