A Banach space with the Schur and the Daugavet property

Details A Banach space with the Schur and the Daugavet property A Banach space with the Schur and the Daugavet property

2003-01-17

arxiv.org/abs/math/0301182v1

Proc. Amer. Math. Soc. 132, no.6, 1765-1773 (2004)

Mathematics

Functional Analysis

10 pages

Scientific paper

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.

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