
Journal of Convex Analysis 20 (2013), No. 2, 439452 Copyright Heldermann Verlag 2013 Remarks on Diameter 2 Properties Trond Abrahamsen Dept. of Mathematics, Agder University, Servicebox 422, 4604 Kristiansand, Norway Trond.A.Abrahamsen@uia.no Vegard Lima Aalesund University College, Postboks 1517, 6025 Aalesund, Norway Vegard.Lima@gmail.com Olav Nygaard Dept. of Mathematics, Agder University, Servicebox 422, 4604 Kristiansand, Norway Olav.Nygaard@uia.no If X is an infinitedimensional uniform algebra, if X has the Daugavet property or if X is a proper Membedded 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 l_{p}sums of diameter 2 spaces does not ruin diameter 2 structure. Keywords: Diameter 2, slice, Daugavet property, Membedded, uniform algebra. MSC: 46B20, 46B22 [ Fulltextpdf (149 KB)] for subscribers only. 