Curvature tensors whose Jacobi or Szabo operator is nilpotent on null vectors

We show that any $k$ Osserman Lorentzian algebraic curvature tensor has constant sectional curvature and give an elementary proof that any local 2 point homogeneous Lorentzian manifold has constant sectional curvature. We also show that a Szab\'o Lorentzian covariant derivative algebraic curvature tensor vanishes.