{"paper":{"title":"Analogs of Cuntz algebras on $L^p$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"N. Christopher Phillips","submitted_at":"2012-01-20T01:19:25Z","abstract_excerpt":"For $d = 2, 3, \\ldots$ and $p \\in [1, \\infty),$ we define a class of representations $\\rho$ of the Leavitt algebra $L_d$ on spaces of the form $L^p (X, \\mu),$ which we call the spatial representations. We prove that for fixed $d$ and $p,$ the Banach algebra ${{\\mathcal{O}}_{d}^{p}}$ obtained as the closure of the image of $L_d$ under the representation $\\rho$ is the same for all spatial representations $\\rho.$ When $p = 2,$ we recover the usual Cuntz algebra ${\\mathcal{O}}_{d}.$ We give a number of equivalent conditions for a representation to be spatial. We show that for distinct $p_1$ and $p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4196","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"}