{"paper":{"title":"Property (T) for Banach algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.OA"],"primary_cat":"math.FA","authors_text":"Emilie Mai Elki{\\ae}r, Sanaz Pooya","submitted_at":"2023-10-27T13:26:55Z","abstract_excerpt":"We define and study the notion of property $(\\rm T)$ for Banach algebras, generalizing the one from $C^*$-algebras. For a second countable locally compact group $G$ and a given family of Banach spaces $\\mathcal E$, we prove that our Banach algebraic property $(\\rm{T}_{\\mathcal E})$ of the symmetrized pseudofunction algebras $F^*_{\\mathcal E}(G)$ characterizes the Banach property $(\\rm{T}_{\\mathcal E})$ of Bader, Furman, Gelander and Monod for groups. In case $G$ is a discrete group and $\\mathcal E$ is the class of $L^p$-spaces for $1\\leq p < \\infty$, we also achieve the analogue characterizati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.18136","kind":"arxiv","version":2},"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/2310.18136/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"}