Finite sums of projections in purely infinite simple C*-algebras with torsion K_0

TL;DR

This paper characterizes when positive elements in purely infinite simple C*-algebras with torsion K_0 can be expressed as finite sums of projections, showing it occurs only if the element is a projection or has norm greater than one.

Contribution

It provides a complete characterization of finite sums of projections in purely infinite simple C*-algebras with torsion K_0, extending understanding of their structure.

Findings

Positive elements are sums of projections iff they are projections or have norm > 1

Characterization applies specifically to algebras with torsion K_0

Advances the structural understanding of purely infinite simple C*-algebras

Abstract

Assume that A is a purely infinite simple C*-algebra whose K_0 is a torsion group, namely, contains no free element. Then a positive element a in A can be written as a finite sum of projections in A if and only if either a is a projection or the norm ||a||>1.