## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Preservation of properties in nonstandard hulls of $C^*$--algebras

Stefano Baratella

#### Abstract

IWe 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 1 (2015), 119-142.

Dates
First available in Project Euclid: 20 March 2015

https://projecteuclid.org/euclid.bbms/1426856863

Digital Object Identifier
doi:10.36045/bbms/1426856863

Mathematical Reviews number (MathSciNet)
MR3325726

Zentralblatt MATH identifier
1336.46062

Keywords
nonstandard hull $C^*$-algebra

#### Citation

Baratella, Stefano. Preservation of properties in nonstandard hulls of $C^*$--algebras. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 1, 119--142. doi:10.36045/bbms/1426856863. https://projecteuclid.org/euclid.bbms/1426856863