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Traces on ultrapowe...
Traces on ultrapowers of C*-algebras
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- Antoine, Ramon (författare)
- Universitat Autonoma de Barcelona (UAB)
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- Perera, Francesc (författare)
- Universitat Autonoma de Barcelona (UAB)
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- Robert, Leonel (författare)
- University of Louisiana at Lafayette
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- Thiel, Hannes, 1982 (författare)
- Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- 2024
- 2024
- Engelska.
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Ingår i: Journal of Functional Analysis. - 0022-1236 .- 1096-0783. ; 286:8
- Relaterad länk:
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https://research.cha... (primary) (free)
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https://research.cha...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- Using Cuntz semigroup techniques, we characterize when limit traces are dense in the space of all traces on a free ultrapower of a C*-algebra. More generally, we consider density of limit quasitraces on ultraproducts of C*-algebras. Quite unexpectedly, we obtain as an application that every simple C*-algebra that is (m,n)-pure in the sense of Winter is already pure. As another application, we provide a partial verification of the first Blackadar–Handelman conjecture on dimension functions. Crucial ingredients in our proof are new Hahn–Banach type separation theorems for noncancellative cones, which in particular apply to the cone of extended-valued traces on a C*-algebra.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- C -algebras ⁎
- Ultraproducts
- Cuntz semigroups
- Traces
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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