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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Subspaces of almost Daugavet spaces


Author: Simon Lücking
Journal: Proc. Amer. Math. Soc. 139 (2011), 2777-2782
MSC (2010): Primary 46B04
Published electronically: December 28, 2010
MathSciNet review: 2801618
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Abstract: We study the almost Daugavet property, a generalization of the Daugavet property. We analyze what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is that if $ Z$ is a closed subspace of a separable almost Daugavet space $ X$ such that the quotient space $ X/Z$ contains no copy of $ \ell_1$, then $ Z$ has the almost Daugavet property too.


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Additional Information

Simon Lücking
Affiliation: Department of Mathematics, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
Email: simon.luecking@fu-berlin.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10722-0
PII: S 0002-9939(2010)10722-0
Keywords: Daugavet property
Received by editor(s): July 17, 2010
Published electronically: December 28, 2010
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.