Abstract
Dissipative linear mappings Z defined on the dense union of an increasing sequence of closed subspaces E n of a Banach space E are studied. It is shown that Z is the pregenerator of a contraction semigroup on E provided that sup ∥ Q nZ ¦ E n ∥ < ∞ where Q n is the quotient map of E onto E E n . This generalises results of Kishimoto and Jørgensen.
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