In this note we present a new sufficient condition which guarantees
martingale approximation and central limit theorem a la Kipnis-Varadhan to hold
for additive functionals of Markov processes. This condition which we call the
relaxed sector condition (RSC) generalizes the strong sector condition (SSC)
and the graded sector condition (GSC) in the case when the self-adjoint part of
the infinitesimal generator acts diagonally in the grading. The main advantage
being that the proof of the GSC in this case is more transparent and less
computational than in the original versions. We also hope that the RSC may have
direct applications where the earlier sector conditions don't apply. So far we
don't have convincing examples in this direction.Comment: 11 page
