Geodesic
Remarks on Diameter 2 Properties
Journal of convex analysis, Tome 20 (2013) no. 2, pp. 439-452 Cet article a éte moissonné depuis la source Heldermann Verlag

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If X is an infinite-dimensional uniform algebra, if X has the Daugavet property or if X is a proper M-embedded space, every relatively weakly open subset of the unit ball of the Banach space X is known to have diameter 2, i.e., X has the diameter 2 property. We prove that in these three cases even every finite convex combination of relatively weakly open subsets of the unit ball have diameter 2. Further, we identify new examples of spaces with the diameter 2 property outside the formerly known cases; in particular we observe that forming lp-sums of diameter 2 spaces does not ruin diameter 2 structure.
Classification : 46B20, 46B22
Mots-clés : Diameter 2, slice, Daugavet property, M-embedded, uniform algebra 
@article{JCA_2013_20_2_JCA_2013_20_2_a6,
     author = {T. Abrahamsen and V. Lima and O. Nygaard},
     title = {Remarks on {Diameter} 2 {Properties}},
     journal = {Journal of convex analysis},
     pages = {439--452},
     year = {2013},
     volume = {20},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_2_JCA_2013_20_2_a6/}
}
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T. Abrahamsen; V. Lima; O. Nygaard. Remarks on Diameter 2 Properties. Journal of convex analysis, Tome 20 (2013) no. 2, pp. 439-452. http://geodesic.mathdoc.fr/item/JCA_2013_20_2_JCA_2013_20_2_a6/