Diametral strong diameter two property of Banach spaces is stable under direct sums with 1-norm

摘要

We prove that the diametral strong diameter 2 property of a Banach space(meaning that, in convex combinations of relatively weakly open subsets of itsunit 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 2property equipped with the 1-norm has again this property.