{"paper":{"title":"Some classes of smooth bimodules over II$_1$ factors and their associated 1-cohomology spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jesse Peterson, Patrick Hiatt, Sorin Popa","submitted_at":"2023-04-13T03:27:30Z","abstract_excerpt":"We study several classes of Banach bimodules over a II$_1$ factor $M$, endowed with topologies that make them \"smooth\" with respect to $L^p$-norms implemented by the trace on $M$. Letting $M\\subset \\B= \\B(L^2M)$, and $2\\leq p < \\infty$, we consider: $(1)$ the space $\\B(p)$, obtained as the completion of $\\B$ in the norm \\[ \\vertiii{T}_p := \\sup \\{|\\varphi(T)| \\mid \\varphi \\in \\B^*, \\sup\\{|\\varphi(xYz)| \\mid Y\\in (\\B)_1, x, z \\in M\\cap (L^pM)_1\\} \\leq 1 \\}; \\] $(2)$ the subspace $\\K(p)\\subset \\B(p)$, obtained as the closure in $\\B(p)$ of the space of compact operators $\\K(L^2M)$; $(3)$ the spac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.06242","kind":"arxiv","version":4},"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/2304.06242/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"}