ABSTRACT
A comparison with Theorem 2.3 shows that the proof of Theorem 3.4 is essentia.lly the same as in the case of the space C. The only difference consists in the fact that the convergence of the operator series for U(t, T), uniformly on every bounded subinterval of J, is proved for the series '(2.32) in the norm of U(1, 00), and for the series (3.51) in the norm of 3p • Since U(1,00) = 300' Theorem 3.4 is more general than Theorem 2.3, at least forma.lly. It is worth mentioning, however, that Theorem 2.3 covers a.ll strongly continuous operator functions with values in .c(C), while Theorem 3.4 applies only (except for the "degenerate" cases p = 1 and p =00) to restricted classes of strongly continuous operator functions in Lp , n~ely those which are actually representable as regular integral operators in Lp•
