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A Banach space with the Schur and the Daugavet property
Author(s):
Vladimir
Kadets;
Dirk
Werner
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1765-1773.
MSC (2000):
Primary 46B04;
Secondary 46B20, 46M07
Posted:
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  -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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Banach spaces with the Daugavet property.
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Additional 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-14195 Berlin, Germany
Email:
vova1kadets@yahoo.com, kadets@math.fu-berlin.de
Dirk
Werner
Affiliation:
Department of Mathematics, Freie Universität Berlin, Arnimallee~2--6, D-14195 Berlin, Germany
Email:
werner@math.fu-berlin.de
DOI:
10.1090/S0002-9939-03-07278-2
PII:
S 0002-9939(03)07278-2
Keywords:
Daugavet property,
Schur property,
ultraproducts of Banach spaces
Received by editor(s):
February 13, 2003
Posted:
October 24, 2003
Additional Notes:
The work of the first author was supported by a fellowship from the {\it Alexander-von-Humboldt Stiftung}.
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2003,
American Mathematical Society
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