{"paper":{"title":"Schur Multipliers of $C^*$-algebras, group-invariant compactification and applications to amenability and percolation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.OA","authors_text":"Chiranjib Mukherjee, Konstantin Recke","submitted_at":"2022-11-21T12:48:26Z","abstract_excerpt":"Let $\\Gamma$ be a countable discrete group. Given any sequence $(f_n)_{n\\geq 1}$ of $\\ell^p$-normalized functions ($p\\in [1,2)$), consider the associated positive definite matrix coefficients $\\langle f_n, \\rho(\\cdot) f_n\\rangle$ of the right regular representation $\\rho$. We construct an orthogonal decomposition of the corresponding {\\it Schur multipliers} on the reduced group $C^*$-algebra or the uniform Roe algebra of $\\Gamma$. We identify this decomposition explicitly via the limit points of the orbits $(\\widetilde f_n)_{n\\geq 1}$ in the group-invariant compactification of the quotient spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.11411","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.11411/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}