Frechet AL-spaces have the Dunford-Pettis property

A Frechet lattice E is an AL-space if its topology can be defined by a family of lattice seminorms that are additive in the positive cone of E. Grothendieck proved that AL-Banach spaces have the Dunford-Pettis property. This result was recently extended by Fernandez and Naranjo to AL-Frechet spaces with a continuous norm and weak order unit. In this note we show how to remove both hypotheses.