  In the algebraic context, we show that null Osserman, spacelike Osserman, and
timelike Osserman are equivalent conditions for a model of signature (2,2). We
also classify the null Jordan Osserman models of signature (2,2). In the
geometric context, we show that a pseudo-Riemannian manifold of signature (2,2)
is null Jordan Osserman if and only if either it has constant sectional
curvature or it is locally a complex space form.
