The goal of this paper is to find out under which conditions the resolvent Κ(λ, Α) of the generator A of a positive semigroup T = (T(f)) t^Q on the space L P (Q) (l < p < oo) is an integral operator. For this purpose we investigate the integral representability of some integrals of operator-valued functions (Theorems 2.1 and 2.10).
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