Norm Continuity for t)0.of Propagators of Arbitrary Order Abstract Differential Equations in Hilbert Spaces*

Let ACPn.,u n. t.q nkys01Aku k. t.s0 tG0., u k. 0.suk 0FkFny1. be strongly wellposed where the Ak 0FkFny1.are densely defined closed linear operators in a Hilbert space. Let Sk t. 0FkFny1. be the propagators of ACPn.and Pl slnIq nksy01lkAk. It is shown thatSk k. t. ;0FkFny1. is norm continuous for t)0 if and only if ny1 y1 lim t qiv P s0, . 0 tqiv0