Nonstandard Hulls of C*-Algebras

Abstract

We study properties of C*-algebras obtained from the nonstandard hull construction (a generalization of the ultraproduct of C*-algebras). Among others, we prove that the properties of being an infinite and a properly infinite C*-algebra are both preserved and reflected by the nonstandard hull construction. We also show that the property of being generated by mutually orthogonal projections is preserved by the nonstandard hull. Furthermore, we indicate how a theory of weights can be developed in a nonstandard hull. Eventually we provide a few examples of standard results that follow from the nonstandard results previously obtained.