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1. CJM 2012 (vol 65 pp. 331)

Kadets, Vladimir; Martín, Miguel; Merí, Javier; Werner, Dirk
Lushness, Numerical Index 1 and the Daugavet Property in Rearrangement Invariant Spaces
We show that for spaces with 1-unconditional bases lushness, the alternative Daugavet property and numerical index 1 are equivalent. In the class of rearrangement invariant (r.i.) sequence spaces the only examples of spaces with these properties are $c_0$, $\ell_1$ and $\ell_\infty$. The only lush r.i. separable function space on $[0,1]$ is $L_1[0,1]$; the same space is the only r.i. separable function space on $[0,1]$ with the Daugavet property over the reals.

Keywords:lush space, numerical index, Daugavet property, Köthe space, rearrangement invariant space
Categories:46B04, 46E30

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