{"paper":{"title":"Algebras of diagonal operators of the form scalar-plus-compact are Calkin algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Tolias, Daniele Puglisi, Pavlos Motakis","submitted_at":"2017-11-03T21:35:10Z","abstract_excerpt":"For every Banach space $X$ with a Schauder basis consider the Banach algebra $\\mathbb{R} I\\oplus\\mathcal{K}_\\mathrm{diag}(X)$ of all diagonal operators that are of the form $\\lambda I + K$. We prove that $\\mathbb{R} I\\oplus\\mathcal{K}_\\mathrm{diag}(X)$ is a Calkin algbra i.e., there exists a Banach space $\\mathcal{Y}_X$ so that the Calkin algebra of $\\mathcal{Y}_X$ is isomorphic as a Banach algebra to $\\mathbb{R} I\\oplus\\mathcal{K}_\\mathrm{diag}(X)$. Among other applications of this theorem we obtain that certain hereditarily indecomposable spaces and the James spaces $J_p$ and their duals end"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01340","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"}