{"paper":{"title":"k-Extreme Points in Symmetric Spaces of Measurable Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anna Kami\\'nska, Ma{\\l}gorzata M. Czerwi\\'nska","submitted_at":"2015-02-13T20:17:55Z","abstract_excerpt":"Let $\\mathcal{M}$ be a semifinite von Neumann algebra with a faithful, normal, semifinite trace $\\tau$ and $E$ be a strongly symmetric Banach function space on $[0,\\tau(1))$. We show that an operator $x$ in the unit sphere of $E\\left(\\mathcal{M},\\tau\\right)$ is $k$-extreme, $k\\in\\mathbb N$, whenever its singular value function $\\mu(x)$ is $k$-extreme and one of the following conditions hold (i) $\\mu(\\infty,x)=\\lim_{t\\to\\infty}\\mu(t,x)=0$ or (ii) $n(x)\\mathcal{M} n(x^*)=0$ and $|x|\\geq \\mu(\\infty,x)s(x)$, where $n(x)$ and $s(x)$ are null and support projections of $x$, respectively. The convers"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04104","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"}