This is an announcement for the paper "Remarks on diameter 2 properties" by Trond Abrahamsen, Vegard Lima, and Olav Nygaard.
Abstract: 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 $\ell_p$-sums of diameter 2 spaces does not ruin diameter 2 structure.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B22
Remarks: To appear in Journal of Convex Analysis
Submitted from: veli@hials.no
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1304.7068
or