This is an announcement for the paper “Diametral strong diameter two property of Banach spaces is stable under direct sums with $1$-norm” by Rainis Haller, Katrlin Pirk and Mart Poldvere.

Abstract: We prove that the diametral strong diameter $2$ property of a Banach space (meaning that, in convex combinations of relatively weakly open subsets of its unit ball, every point has an "almost diametral" point) is stable under $1$-sums, i.e., the direct sum of two spaces with the diametral strong diameter $2$ property equipped with the $1$-norm has again this property.

The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.08082