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

2016/03/26 by R. Haller, Haller, Rainis, Katriin Pirk +3
Computer Science · Mathematics · #46B20 #46B22 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1603.08082

openalex publication_date 2016/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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