A mean ergodic theorem for resolvent operators

Let {R(t)} _t≥0 be a uniformly bounded strongly continuous resolvent operator for the Volterra equation of convolution typeu=g+k*Au, whereA is a closed and densely defined operator on a Banach spaceX andk is a scalar kernel. We show that whenX is reflexive and that the average given by {R(t)} _t≥0 andk converges on the closed subspace to a bounded projection. This work was partially supported by DICYT 92-33LY and FONDECYT 91-0471