{"paper":{"title":"Cebysev subspaces of JBW*-triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.OA","authors_text":"Akhlaq A. Siddiqui, Antonio M. Peralta, Fatmah B. Jamjoom, Haifa M. Tahlawi","submitted_at":"2014-12-10T08:56:21Z","abstract_excerpt":"We describe the one-dimensional \\v{C}eby\\v{s}\\\"{e}v subspaces of a JBW$^*$-triple $M,$ by showing that for a non-zero element $x$ in $M$, $\\mathbb{C}x$ is a \\v{C}eby\\v{s}\\\"{e}v subspace of $M$ if, and only if, $x$ is a Brown-Pedersen quasi-invertible element in ${M}$. We study the \\v{C}eby\\v{s}\\\"{e}v JBW$^*$-subtriples of a JBW$^*$-triple $M$. We prove that, for each non-zero \\v{C}eby\\v{s}\\\"{e}v JBW$^*$-subtriple $N$ of $M$, then exactly one of the following statements holds: $(a)$ $N$ is a rank one JBW$^*$-triple with dim$(N)\\geq 2$ (i.e. a complex Hilbert space regarded as a type 1 Cartan fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3227","kind":"arxiv","version":2},"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"}