{"paper":{"title":"The compact operators on $c_0$ as a Calkin algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Daniele Puglisi, Pavlos Motakis","submitted_at":"2024-03-07T01:33:38Z","abstract_excerpt":"For a Banach space $X$, let $\\mathcal{L}(X)$ denote the algebra of all bounded linear operators on $X$ and let $\\mathcal{K}(X)$ denote the compact operator ideal in $\\mathcal{L}(X)$. The quotient algebra $\\mathcal{L}(X)/\\mathcal{K}(X)$ is called the Calkin algebra of $X$, and it is denoted $\\mathcal{C}al(X)$. We prove that the unitization of $\\mathcal{K}(c_0)$ is isomorphic as a Banach algebra to the Calkin algebra of some Banach space $\\mathcal{Z}_{\\mathcal{K}(c_0)}$. This Banach space is an Argyros-Haydon sum $(\\oplus_{n=1}^\\infty X_n)_\\mathrm{AH}$ of a sequence of copies $X_n$ of a single A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.04137","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.04137/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"}