Quasi-Affinity in certain Classes of Operators

The family of operators S + V (, C, Re > 0), where V isan injective S-Volterra operator (that is, S, V = V²) and— A — V^–1 generates a uniformly bounded C₀-semigroup,is studied in the context of similarity and of the weaker quasi-affinityrelation. It is shown that S is similar to S + V for all , C,Re > 1, and is a quasi-affine transform of S + tV for allt 0 and 0 < < 1.