Subspaces of almost Daugavet spaces
HTML articles powered by AMS MathViewer
- by Simon Lücking PDF
- Proc. Amer. Math. Soc. 139 (2011), 2777-2782 Request permission
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.References
- Vladimir Kadets, Varvara Shepelska, and Dirk Werner, Quotients of Banach spaces with the Daugavet property, Bull. Pol. Acad. Sci. Math. 56 (2008), no. 2, 131–147. MR 2431006, DOI 10.4064/ba56-2-5
- Vladimir Kadets, Varvara Shepelska, and Dirk Werner, Thickness of the unit sphere, $\ell _1$-types, and the almost Daugavet property (2009), to appear in Houston J. Math., available at http://arxiv.org/abs/0902.4503v1.
- Vladimir M. Kadets, Roman V. Shvidkoy, Gleb G. Sirotkin, and Dirk Werner, Banach spaces with the Daugavet property, Trans. Amer. Math. Soc. 352 (2000), no. 2, 855–873. MR 1621757, DOI 10.1090/S0002-9947-99-02377-6
- J.-L. Krivine and B. Maurey, Espaces de Banach stables, Israel J. Math. 39 (1981), no. 4, 273–295 (French, with English summary). MR 636897, DOI 10.1007/BF02761674
- Robert Whitley, The size of the unit sphere, Canadian J. Math. 20 (1968), 450–455. MR 228997, DOI 10.4153/CJM-1968-041-1
Additional Information
- Simon Lücking
- Affiliation: Department of Mathematics, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
- Email: simon.luecking@fu-berlin.de
- Received by editor(s): July 17, 2010
- Published electronically: December 28, 2010
- Communicated by: Nigel J. Kalton
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2777-2782
- MSC (2010): Primary 46B04
- DOI: https://doi.org/10.1090/S0002-9939-2010-10722-0
- MathSciNet review: 2801618