Abstract
AbstractIt is shown that the spectrum of a positive Reynolds operator on C0(X) is contained in the disc centered at 1/2 with radius 1/2. Moreover, every positive Reynolds operator T with dense range is injective. In this case, the operator D = 1 — T−1 is a densely defined derivation, which generates a one — parameter semigroup of algebra homomorphisms. This semigroup yields an integral representation of T. Along the way, it is proved that a densely defined closed derivation D generates a semigroup if, and only if, R(1, D) exists and is a positive operator.
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