{"paper":{"title":"Admissible sequences for positive operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"David Larson, Victor Kaftal","submitted_at":"2018-01-14T04:34:51Z","abstract_excerpt":"A sequence of scalars is said to be admissible for a positive operator A on a Hilbert space if it is the diagonal of VAV* for some partial isometry V having as domain the closure of the range of A. When A is a projection, the celebrated Kadison's carpenter theorem provides a sufficient condition for a sequence to be admissible for A. We prove that the same condition is sufficient for the sequence to be admissible for A when A is a sum of projections (converging in the SOT). This provides an independent proof of Kadison's carpenter theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04509","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"}