Perturbation of Hausdorff Moment Sequences, and an Application to the Theory of C*-Algebras of Real Rank Zero

Abstract

We investigate the class of unital C*-algebras that admit a unital embedding into every unital C*-algebra of real rank zero, that has no finite-dimensional quotients. We refer to a C*-algebra in this class as an initial object. We show that there are many initial objects, including for example some unital, simple, infinite-dimensional AF-algebras, the Jiang-Su algebra, and the GICAR-algebra. That the GICAR-algebra is an initial object follows from an analysis of Hausdorff moment sequences. It is shown that a dense set of Hausdorff moment sequences belong to a given dense subgroup of the real numbers, and hence that the Hausdorff moment problem can be solved (in a non-trivial way) when the moments are required to belong to an arbitrary simple dimension group (i.e., unperforated simple ordered group with the Riesz decomposition property).