A posteriori error estimation plays an import role for selecting efficient basis sets for the solution of partial differential equations. Often, one is not interested in the error of the approximate solution with respect to some global norm, but rather to improve the error in the value of some target functional computed from it. This is the aim of the so-called Dual Weighted Residual Method (DWR).

Let the PDE under consideration be an eigenvalue problem for some linear operator. We consider an eigenspace of finite dimension of this operator and a functional welldefined on this subspace and the associated eigenvalues. This leads to the question of estimating the error in this functional computed from an approximation to the eigenspace.

After giving a short introduction to the DWR, we will present recent results concerning an error representation to the above problem.