Matches in SemOpenAlex for { <https://semopenalex.org/work/W2152204325> ?p ?o ?g. }
- W2152204325 abstract "We study several notions of ultraproducts of von Neumann algebras from a unifying viewpoint. In particular, we show that for a sigma-finite von Neumann algebra $M$, the ultraproduct $M^{omega}$ introduced by Ocneanu is a corner of the ultraproduct $prod^{omega}M$ introduced by Groh and Raynaud. Using this connection, we show that the ultraproduct action of the modular automorphism group of a normal faithful state $varphi$ of $M$ on the Ocneanu ultraproduct is the modular automorphism group of the ultrapower state ($sigma_t^{varphi^{omega}}=(sigma_t^{varphi})^{omega}$). Applying these results, we obtain several phenomena of the Ocneanu ultraproduct of type III factors, which are not present in the tracial ultraproducts. For instance, it turns out that the ultrapower $M^{omega}$ of a Type III$_0$ factor is never a factor. Moreover we settle in the affirmative a recent problem by Ueda about the connection between the relative commutant of $M$ in $M^{omega}$ and Connes' asymptotic centralizer algebra $M_{omega}$." @default.
- W2152204325 created "2016-06-24" @default.
- W2152204325 creator A5025323920 @default.
- W2152204325 creator A5084475536 @default.
- W2152204325 date "2012-12-21" @default.
- W2152204325 modified "2023-09-27" @default.
- W2152204325 title "Ultraproducts of von Neumann algebras" @default.
- W2152204325 cites W1524878283 @default.
- W2152204325 cites W1533213248 @default.
- W2152204325 cites W153850935 @default.
- W2152204325 cites W1556158080 @default.
- W2152204325 cites W1563415619 @default.
- W2152204325 cites W1572232119 @default.
- W2152204325 cites W1592596064 @default.
- W2152204325 cites W1596434689 @default.
- W2152204325 cites W1829449347 @default.
- W2152204325 cites W1919779633 @default.
- W2152204325 cites W1965686555 @default.
- W2152204325 cites W1976554830 @default.
- W2152204325 cites W1979018784 @default.
- W2152204325 cites W1981800389 @default.
- W2152204325 cites W1983046429 @default.
- W2152204325 cites W1985844586 @default.
- W2152204325 cites W2002212138 @default.
- W2152204325 cites W2019601500 @default.
- W2152204325 cites W2028188838 @default.
- W2152204325 cites W2045658060 @default.
- W2152204325 cites W2048971487 @default.
- W2152204325 cites W2055178055 @default.
- W2152204325 cites W2056181033 @default.
- W2152204325 cites W2074201888 @default.
- W2152204325 cites W2078963448 @default.
- W2152204325 cites W2080327019 @default.
- W2152204325 cites W2080628627 @default.
- W2152204325 cites W2083886939 @default.
- W2152204325 cites W2085026304 @default.
- W2152204325 cites W2096750502 @default.
- W2152204325 cites W2111967948 @default.
- W2152204325 cites W2119756346 @default.
- W2152204325 cites W2140050210 @default.
- W2152204325 cites W2171661581 @default.
- W2152204325 cites W2276473350 @default.
- W2152204325 cites W2318358641 @default.
- W2152204325 cites W2319090957 @default.
- W2152204325 cites W2320355311 @default.
- W2152204325 cites W2323990519 @default.
- W2152204325 cites W2494415787 @default.
- W2152204325 cites W2562293972 @default.
- W2152204325 cites W3038830718 @default.
- W2152204325 cites W3098725798 @default.
- W2152204325 cites W3099715667 @default.
- W2152204325 cites W3101441544 @default.
- W2152204325 cites W3101461530 @default.
- W2152204325 cites W597827420 @default.
- W2152204325 hasPublicationYear "2012" @default.
- W2152204325 type Work @default.
- W2152204325 sameAs 2152204325 @default.
- W2152204325 citedByCount "2" @default.
- W2152204325 countsByYear W21522043252013 @default.
- W2152204325 crossrefType "posted-content" @default.
- W2152204325 hasAuthorship W2152204325A5025323920 @default.
- W2152204325 hasAuthorship W2152204325A5084475536 @default.
- W2152204325 hasConcept C118712358 @default.
- W2152204325 hasConcept C138885662 @default.
- W2152204325 hasConcept C153408630 @default.
- W2152204325 hasConcept C167930466 @default.
- W2152204325 hasConcept C18903297 @default.
- W2152204325 hasConcept C202444582 @default.
- W2152204325 hasConcept C2777299769 @default.
- W2152204325 hasConcept C2779557605 @default.
- W2152204325 hasConcept C33923547 @default.
- W2152204325 hasConcept C41895202 @default.
- W2152204325 hasConcept C75174853 @default.
- W2152204325 hasConcept C80469333 @default.
- W2152204325 hasConcept C86803240 @default.
- W2152204325 hasConceptScore W2152204325C118712358 @default.
- W2152204325 hasConceptScore W2152204325C138885662 @default.
- W2152204325 hasConceptScore W2152204325C153408630 @default.
- W2152204325 hasConceptScore W2152204325C167930466 @default.
- W2152204325 hasConceptScore W2152204325C18903297 @default.
- W2152204325 hasConceptScore W2152204325C202444582 @default.
- W2152204325 hasConceptScore W2152204325C2777299769 @default.
- W2152204325 hasConceptScore W2152204325C2779557605 @default.
- W2152204325 hasConceptScore W2152204325C33923547 @default.
- W2152204325 hasConceptScore W2152204325C41895202 @default.
- W2152204325 hasConceptScore W2152204325C75174853 @default.
- W2152204325 hasConceptScore W2152204325C80469333 @default.
- W2152204325 hasConceptScore W2152204325C86803240 @default.
- W2152204325 hasLocation W21522043251 @default.
- W2152204325 hasOpenAccess W2152204325 @default.
- W2152204325 hasPrimaryLocation W21522043251 @default.
- W2152204325 hasRelatedWork W1770265315 @default.
- W2152204325 hasRelatedWork W1806851539 @default.
- W2152204325 hasRelatedWork W1809936056 @default.
- W2152204325 hasRelatedWork W2043887126 @default.
- W2152204325 hasRelatedWork W2057150397 @default.
- W2152204325 hasRelatedWork W2145945838 @default.
- W2152204325 hasRelatedWork W2411655566 @default.
- W2152204325 hasRelatedWork W2954986749 @default.
- W2152204325 hasRelatedWork W2963555735 @default.