Infinite multiplier projections and dichotomy of C* -algebras

Abstract

We study infiniteness of multiplier projections of a stabilized C* -algebra and the connection to dichotomy of a C* -algebra A in the sense of A being either stably finite or purely infinite. The main result is the reduction of the dichotomy problem for real rank zero algebras to a ·property on multiplier projections, which could possibly hold for general separable C* -algebras.