Spacelike Jordan Osserman algebraic curvature tensors in the higher   signature setting
  Let $R$ be an algebraic curvature tensor on a vector space of signature $(p,q)$ defining a spacelike Jordan Osserman Jacobi operator $\JJ_R$. We show that the eigenvalues of $\JJ_R$ are real and that $\JJ_R$ is diagonalizable if $p<q$. 
Peter B. Gilkey and Raina Ivanova