{"paper":{"title":"Extensions and Dilations for $C^*$-dynamical Systems","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Baruch Solel, Paul S. Muhly","submitted_at":"2005-09-22T06:16:58Z","abstract_excerpt":"Let $A$ be a unital $C^*$-algebra and $\\alpha$ be an injective, unital endomorphism of $A$. A covariant representation of $(A,\\alpha)$ is a pair $(\\pi,T)$ consisting of a $C^*$-representation $\\pi$ of $A$ on a Hilbert space $H$ and a contraction $T$ in $B(H)$ satisfying $T\\pi(\\alpha(a))=\\pi(a)T$.\n  It follows from more general results of ours that such a covariant representation can be extended to a covariant representation $(\\rho,V)$ (on a larger space $K$) such that $V$ is a coisometry and it can be dilated to a covariant representation $(\\sigma,U)$ (on a larger space $K_1$) with $U$ unitary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0509506","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"}