Abstract
In this paper we prove some uniform convergence theorems for operators on a Grothendieck space with the Dunford-Pettis property. As consequences we obtain 1) that on such spaces (in particular on L ∞ and H ∞ (D)) every C 0 -semigroup is uniformly continous, 2) that on such spaces the strong ergodic theorem becomes a uniform ergodic theorem, and 3) Dean's result that such a space does not have a Schauder decomposition.
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