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arXiv · 1603.08082

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

Rainis Haller·Katriin Pirk·Märt Põldvere
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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.

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Rainis Haller, Katriin Pirk, Märt Põldvere. 2016-03-26. Diametral strong diameter two property of Banach spaces is stable under direct sums with 1-norm. https://arxiv.org/abs/1603.08082

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