Geodesic
Lushness, Numerical Index 1 and the Daugavet Property in Rearrangement Invariant Spaces
Canadian journal of mathematics, Tome 65 (2013) no. 2, pp. 331-348

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DOI

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 $\left[ 0,1 \right]$ is ${{L}_{1}}\left[ 0,1 \right]$ ; the same space is the only r.i. separable function space on $\left[ 0,1 \right]$ with the Daugavet property over the reals.
DOI : 10.4153/CJM-2011-096-2
Mots-clés : 46B04, 46E30, lush space, numerical index, Daugavet property, Köthe space, rearrangement invariant space 
Kadets, Vladimir; Martín, Miguel; Merí, Javier; Werner, Dirk. Lushness, Numerical Index 1 and the Daugavet Property in Rearrangement Invariant Spaces. Canadian journal of mathematics, Tome 65 (2013) no. 2, pp. 331-348. doi: 10.4153/CJM-2011-096-2
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     journal = {Canadian journal of mathematics},
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     year = {2013},
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