Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 22, Number 1 (2015), 119-142.
Preservation of properties in nonstandard hulls of $C^*$--algebras
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.
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 1 (2015), 119-142.
First available in Project Euclid: 20 March 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46S20: Nonstandard functional analysis [See also 03H05]
Secondary: 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05] 26E35: Nonstandard analysis [See also 03H05, 28E05, 54J05] 46L05: General theory of $C^*$-algebras
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