Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Stefano Baratella

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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

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

First available in Project Euclid: 20 March 2015

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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

nonstandard hull $C^*$-algebra


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

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