Approximating semigroups and the consistency of difference schemes
Gilbert Strang · Proceedings of the American Mathematical Society · 1969
What hypotheses on the generators Lk ensure that the corresponding semigroups etLk converge to a given semigroup etL? Assuming these are Co semigroups on a common Banach space CB, several alternative hypotheses have been proposed. We want to compare, and in fact to order, the three most important alternatives. The possibility of such an ordering is a question which was asked by Trotter [1], and appears to have remained unanswered. Convergence is given the standard interpretation: For everyf cI and T>0,