{"paper":{"title":"Absolutely compatible pair of elements in a von Neumann algebra-II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Anil Kumar Karn","submitted_at":"2019-06-24T04:54:34Z","abstract_excerpt":"Let $A$ be a unital C$^*$-algebra with unity $1_A$. A pair of elements $0 \\le a, b \\le 1_A$ in $A$ is said to be \\emph{absolutely compatible} if, $\\vert a - b \\vert + \\vert 1_A - a - b \\vert = 1_A.$ In this paper we provide a complete description of absolutely compatible pair of strict elements in a von Neumann algebra. The end form of such a pair has a striking resemblance with that of a `generic pair' of projections on a complex Hilbert space introduced by Halmos."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09723","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"}