{"paper":{"title":"The noncommutative Choquet boundary","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"William Arveson","submitted_at":"2007-01-11T19:16:35Z","abstract_excerpt":"Let S be an operator system -- a self-adjoint linear subspace of a unital C*-algebra A such that contains 1 and A=C*(S) is generated by S. A boundary representation for S is an irreducible representation \\pi of C*(S) on a Hilbert space with the property that $\\pi\\restriction_S$ has a unique completely positive extension to C*(S). The set $\\partial_S$ of all (unitary equivalence classes of) boundary representations is the noncommutative counterpart of the Choquet boundary of a function system $S\\subseteq C(X)$ that separates points of X.\n  It is known that the closure of the Choquet boundary of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701329","kind":"arxiv","version":4},"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"}