{"paper":{"title":"Semicrossed products of operator algebras and their C*-envelopes","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Elias Katsoulis, Evgenios Kakariadis","submitted_at":"2010-08-13T19:10:46Z","abstract_excerpt":"Let $\\A$ be a unital operator algebra and let $\\alpha$ be an automorphism of $\\A$ that extends to a *-automorphism of its $\\ca$-envelope $\\cenv (\\A)$. In this paper we introduce the isometric semicrossed product $\\A \\times_{\\alpha}^{\\is} \\bbZ^+ $ and we show that $\\cenv(\\A \\times_{\\alpha}^{\\is} \\bbZ^+) \\simeq \\cenv (\\A) \\times_{\\alpha} \\bbZ$. In contrast, the $\\ca$-envelope of the familiar contractive semicrossed product $\\A \\times_{\\alpha} \\bbZ^+ $ may not equal $\\cenv (\\A) \\times_{\\alpha} \\bbZ$. Our main tool for calculating $\\ca$-envelopes for semicrossed products is the concept of a relati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2374","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"}