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EnglishWe extend the nonstandard hull construction of Luxemburg and we show that the proposed extension covers various other constructions such as the tracial and the weak nonstandard hull. We provide a novel proof that the tracial nonstandard hull of an internal von Neumann algebra is itself a von Neumann algebra. We prove that some extensively studied properties of C*-algebras are preserved and reflected by the nonstandard hull construction. Eventually, we show how to obtain hull--like representations of the two K--groups associated to the nonstandard hull of an internal C*-algebra.
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| Titolo: | Preservation of properties in nonstandard hulls of C*-algebras |
| Autori Unitn: | |
| Anno di pubblicazione: | 2015 |
| Titolo del periodico: | |
| Abstract: | We extend the nonstandard hull construction of Luxemburg and we show that the proposed extension covers various other constructions such as the tracial and the weak nonstandard hull. We provide a novel proof that the tracial nonstandard hull of an internal von Neumann algebra is itself a von Neumann algebra. We prove that some extensively studied properties of C*-algebras are preserved and reflected by the nonstandard hull construction. Eventually, we show how to obtain hull--like representations of the two K--groups associated to the nonstandard hull of an internal C*-algebra. |
| Handle: | http://hdl.handle.net/11572/101252 |
| Appare nelle tipologie: | 03.1 Articolo su rivista (Journal article) |
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