{"paper":{"title":"Completely bounded isomorphisms of operator algebras and similarity to complete isometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Rapha\\\"el Clou\\^atre","submitted_at":"2014-01-03T22:44:12Z","abstract_excerpt":"A well-known theorem of Paulsen says that if $\\mathcal{A}$ is a unital operator algebra and $\\phi:\\mathcal{A}\\to B(\\mathcal{H})$ is a unital completely bounded homomorphism, then $\\phi$ is similar to a completely contractive map $\\phi'$. Motivated by classification problems for Hilbert space contractions, we are interested in making the inverse $\\phi'^{-1}$ completely contractive as well whenever the map $\\phi$ has a completely bounded inverse. We show that there exist invertible operators $X$ and $Y$ such that the map $$ XaX^{-1}\\mapsto Y\\phi(a)Y^{-1} $$ is completely contractive and is \"almo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0748","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"}