A Banach space with the Schur and the Daugavet property
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- by Vladimir Kadets and Dirk Werner
- Proc. Amer. Math. Soc. 132 (2004), 1765-1773
- DOI: https://doi.org/10.1090/S0002-9939-03-07278-2
- Published electronically: October 24, 2003
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Abstract:
We show that a minor refinement of the Bourgain-Rosenthal construction of a Banach space without the Radon-Nikodým 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.References
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Bibliographic Information
- Vladimir Kadets
- Affiliation: Faculty of Mechanics and Mathematics, Kharkov National University, pl. Svobody 4, 61077 Kharkov, Ukraine
- Address at time of publication: Department of Mathematics, Freie Universität Berlin, Arnimallee 2–6, D-14 195 Berlin, Germany
- MR Author ID: 202226
- ORCID: 0000-0002-5606-2679
- Email: vova1kadets@yahoo.com, kadets@math.fu-berlin.de
- Dirk Werner
- Affiliation: Department of Mathematics, Freie Universität Berlin, Arnimallee 2–6, D-14 195 Berlin, Germany
- Email: werner@math.fu-berlin.de
- Received by editor(s): February 13, 2003
- Published electronically: October 24, 2003
- Additional Notes: The work of the first author was supported by a fellowship from the Alexander-von-Humboldt Stiftung.
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1765-1773
- MSC (2000): Primary 46B04; Secondary 46B20, 46M07
- DOI: https://doi.org/10.1090/S0002-9939-03-07278-2
- MathSciNet review: 2051139