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.

Preservation of properties in nonstandard hulls of C*-algebras / Baratella, Stefano. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - STAMPA. - 2015 - 22:1(2015), pp. 119-142.

Preservation of properties in nonstandard hulls of C*-algebras

Baratella, Stefano
2015-01-01

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.
2015
1
Baratella, Stefano
Preservation of properties in nonstandard hulls of C*-algebras / Baratella, Stefano. - In: BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY SIMON STEVIN. - ISSN 1370-1444. - STAMPA. - 2015 - 22:1(2015), pp. 119-142.
File in questo prodotto:
File Dimensione Formato  
PPNSHC*_BBMS.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 603.65 kB
Formato Adobe PDF
603.65 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/101252
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact