{"paper":{"title":"Inner ideals, compact tripotents and \\v{C}eby\\v{s}\\\"ev subtriples of JB$^{*}$-triples and C$^*$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Akhlaq A. Siddiqui, Antonio M. Peralta, Fatmah B. Jamjoom, Haifa M. Tahlawi","submitted_at":"2015-07-26T11:09:45Z","abstract_excerpt":"The aim of this note is to study \\v{C}eby\\v{s}\\\"ev JB$^*$-subtriples of general JB$^*$-triples. It is established that if $F$ is a non-zero \\v{C}eby\\v{s}\\\"ev JB$^*$-subtriple of a JB$^*$-triple $E$, then exactly one of the following statements holds:\\begin{enumerate}\\item $F$ is a rank one JBW$^*$-triple with dim$(F)\\geq 2$ (i.e. a complex Hilbert space regarded as a type 1 Cartan factor). Moreover, $F$ may be a closed subspace of arbitrary dimension and $E$ may have arbitrary rank, \\item $F= \\mathbb{C} e$, where $e$ is a complete tripotent in $E$, \\item $E$ and $F$ are rank two JBW$^*$-triple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07186","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"}