Preprint No. A-03-01

Vladimir Kadets, Dirk Werner

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 $\delta$-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.

Keywords: Daugavet property, Schur property, ultraproducts of Banach spaces

Mathematics Subject Classification (MSC2000): 46B04; 46B20, 46M07

Language: ENG


Contact: Dirk Werner, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (

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