Approximation by elements of finite spectra for C* Algebras of higher real rank

Abstract

In this article, we extend a well known result about real rank zero C* Algebras to higher real rank C* Algebras. The main technique used here is similar to the method in which we approximate continuous functions using projections. What we reach at the end, is similar to the fact that the self-adjoint elements of a real rank zero C* Algebra can be approximated by elements of finite spectrum. We achieve the result for the diagonal of the self-adjoint elements of A^2, where A is a real rank one C* Algebra.