{"paper":{"title":"Conditional positive definiteness as a bridge between k-hyponormality and n-contractivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chafiq Benhida, George R. Exner, Raul E. Curto","submitted_at":"2020-12-20T16:15:01Z","abstract_excerpt":"For sequences $\\alpha \\equiv \\{\\alpha_n\\}_{n=0}^{\\infty}$ of positive real numbers, called weights, we study the weighted shift operators $W_{\\alpha}$ having the property of moment infinite divisibility ($\\mathcal{MID}$); that is, for any $p > 0$, the Schur power $W_{\\alpha}^p$ is subnormal. We first prove that $W_{\\alpha}$ is $\\mathcal{MID}$ if and only if certain infinite matrices $\\log M_{\\gamma}(0)$ and $\\log M_{\\gamma}(1)$ are conditionally positive definite (CPD). Here $\\gamma$ is the sequence of moments associated with $\\alpha$, $M_{\\gamma}(0),M_{\\gamma}(1)$ are the canonical Hankel mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10962","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.10962/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}