{"paper":{"title":"Algebraic orthogonality in $C^{\\ast}$--algebras-II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Anil Kumar Karn","submitted_at":"2017-05-04T23:30:44Z","abstract_excerpt":"We prove the following: Let $A$ be a C$^{\\ast}$-algebra. Then for $a, b \\in A^+ \\setminus\\{ 0 \\}$, we have $a b = 0$ if and only is $\\Vert \\Vert c \\Vert^{-1} c + \\Vert d \\Vert^{-1} d \\Vert = 1$ whenever $0 < c \\le a$ and $0 < d \\le b$ in $A^+$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02046","kind":"arxiv","version":3},"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"}