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dc.contributor.authorBaudier, Florent P.en_US
dc.contributor.authorBraga, Bruno M.en_US
dc.contributor.authorFarah, Ilijasen_US
dc.contributor.authorVignati, Alessandroen_US
dc.contributor.authorWillett, Rufusen_US
dc.date.accessioned2023-11-23T14:39:49Z-
dc.date.available2023-11-23T14:39:49Z-
dc.date.issued2024-
dc.identifier.issn0022-1236-
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/5221-
dc.description.abstractWe study which von Neumann algebras can be embedded into uniform Roe algebras and quasi-local algebras associated to a uniformly locally finite metric space X. Under weak assumptions, these C⁎-algebras contain embedded copies of ∏kMnk(C) for any bounded countable (possibly finite) collection (nk)k of natural numbers; we aim to show that they cannot contain any other von Neumann algebras. One of our main results shows that L∞[0,1] does not embed into any of those algebras, even by a not-necessarily-normal ⁎-homomorphism. In particular, it follows from the structure theory of von Neumann algebras that any von Neumann algebra which embeds into such algebra must be of the form ∏kMnk(C) for some countable (possibly finite) collection (nk)k of natural numbers. Under additional assumptions, we also show that the sequence (nk)k has to be bounded: in other words, the only embedded von Neumann algebras are the “obvious” ones.en_US
dc.publisherElsevieren_US
dc.relation.ispartofJournal of Functional Analysisen_US
dc.subjectCoarse geometry | Uniform Roe algebras | Von Neumann algebrasen_US
dc.titleEmbeddings of von Neumann algebras into uniform Roe algebras and quasi-local algebrasen_US
dc.typeArticleen_US
dc.identifier.doi10.1016/j.jfa.2023.110186-
dc.identifier.scopus2-s2.0-85173544125-
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Artsen_US
dc.relation.firstpage110186-
dc.relation.issue1-
dc.relation.volume286-
dc.description.rank~M21-
item.cerifentitytypePublications-
item.grantfulltextnone-
item.openairetypeArticle-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextNo Fulltext-
crisitem.author.orcid0000-0001-7703-6931-
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