Abstract of a paper by Rainis Haller, Katrlin Pirk and Mart Poldvere
30 Apr
2016
30 Apr
'16
11:27 a.m.
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
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Bentuo Zheng (bzheng)