{"paper":{"title":"Radial multipliers on arbitrary amalgamated free products of finite von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Steven Deprez","submitted_at":"2013-10-29T17:06:59Z","abstract_excerpt":"Let $(M_i)_{i}$ be a (finite or infinite) family of finite von Neumann algebras with a common subalgebra $P$. When $\\varphi:\\IN\\rightarrow\\IC$ is a function, we define the radial multiplier $M_\\varphi$ on the amalgamated free product $M=M_1\\free_P M_2\\free_P\\ldots$ setting $M_{\\varphi}(x)=\\varphi(n)x$ for every reduced expression $x$ of length $n$. In this paper we give a sufficient condition on $\\varphi$ to ensure that the corresponding radial multiplier $M_\\varphi$ is a completely bounded map, and moreover we give an upper bound on its completely bounded norm. Our condition on $\\varphi$ does"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7880","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"}