Simple inductive limit C*-algebras: Spectra and approximations by interval algebras

Abstract

Abstract Suppose that a simple C*-algebra A can be written as an inductive limit of , where Xn,i are finite CW complexes with uniformly bounded dimensions. Such inductive limit C*-algebras are called AH algebras. In this paper, we will prove that for any n and ε > 0, there exists a homomorphism ψn,m: An → Am, which factors through an interval algebra , such that the spectra of ψn,m and the spectra of φn,m can be paired within ε provided that m is large enough. This result is essential for the classification of such simple C*-algebras.