{"paper":{"title":"Banach algebras generated by an invertible isometry of an $L^p$-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Eusebio Gardella, Hannes Thiel","submitted_at":"2014-05-22T01:50:04Z","abstract_excerpt":"We provide a complete description of those Banach algebras that are generated by an invertible isometry of an $L^p$-space together with its inverse. Examples include the algebra $PF_p(\\mathbb{Z})$ of $p$-pseudofunctions on $\\mathbb{Z}$, the commutative $C^*$-algebra $C(S^1)$ and all of its quotients, as well as uncountably many `exotic' Banach algebras.\n  We associate to each isometry of an $L^p$-space, a spectral invariant called `spectral configuration', which contains considerably more information than its spectrum as an operator. It is shown that the spectral configuration describes the is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5589","kind":"arxiv","version":3},"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"}