{"paper":{"title":"Stability of average roughness, octahedrality, and strong diameter 2 properties of Banach spaces with respect to absolute sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Johann Langemets, Rainis Haller, Rihhard Nadel","submitted_at":"2017-02-10T11:43:09Z","abstract_excerpt":"We prove that, if Banach spaces $X$ and $Y$ are $\\delta$-average rough, then their direct sum with respect to an absolute norm $N$ is $\\delta/N(1,1)$-average rough. In particular, for octahedral $X$ and $Y$ and for $p$ in $(1,\\infty)$ the space $X\\oplus_p Y$ is $2^{1-1/p}$-average rough, which is in general optimal. Another consequence is that for any $\\delta$ in $(1,2]$ there is a Banach space which is exactly $\\delta$-average rough. We give a complete characterization when an absolute sum of two Banach spaces is octahedral or has the strong diameter 2 property. However, among all of the abso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03140","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}