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
Available: Pr-A-03-01.ps
Contact: Dirk Werner, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (werner@math.fu-berlin.de)
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