A Banach space with the Schur and the Daugavet property

Vladimir Kadets, Dirk Werner

Published 2003-01-17Version 1

We show that a minor refinement of the Bourgain-Rosenthal construction of a Banach space without the Radon-Nikodym property which contains no bounded $\delta$-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.