A Banach space with the Schur and the Daugavet property
Abstract
We show that a minor refinement of the Bourgain-Rosenthal construction of a Banach space without the Radon-Nikodym property which contains no bounded δ-trees yields a space with the Daugavet property and the Schur property. Using this example we answer some open questions on the structure of such spaces; in particular we show that the Daugavet property is not inherited by ultraproducts.
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