{"paper":{"title":"A hierarchy of Banach spaces with $C(K)$ Calkin Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniele Puglisi, Despoina Zisimopoulou, Pavlos Motakis","submitted_at":"2014-07-30T15:04:16Z","abstract_excerpt":"For every well founded tree $\\mathcal{T}$ having a unique root such that every non-maximal node of it has countable infinitely many immediate successors, we construct a $\\mathcal{L}_\\infty$-space $X_{\\mathcal{T}}$. We prove that for each such tree $\\mathcal{T}$, the Calkin algebra of $X_{\\mathcal{T}}$ is homomorphic to $C(\\mathcal{T})$, the algebra of continuous functions defined on $\\mathcal{T}$, equipped with the usual topology. We use this fact to conclude that for every countable compact metric space $K$ there exists a $\\mathcal{L}_\\infty$-space whose Calkin algebra is isomorphic, as a Ban"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8073","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":""},"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"}