ABSTRACT
Since II ~fllo < IIfllo, the seminorm, I · Ik' can be replaced by the norm, II · Ilk' in (2.8), so that II Ttll k < exp(Akt).
Theorem 1 is similar to a result of Ethier [7, Theorem I], in which C k takes the place of our D k • Ethier's proof, involving a judicious combination of semigroup and martingale methods, is quite different from ours. Unlike our result, Ethier's is not restricted to finite intervals I. In order to apply our result to infinite intervals, it is necessary to make a preliminary spatial transformation of the type used in the proof of Lemma 6 in §7.
