In mathematics, a projectionless C*-algebra is a C*-algebra with no projections besides 0 and 1. The first simple infinite dimensional C*-algebra with this property was constructed by Bruce Blackadar. Today other examples are available, such as the reduced group C*-algebra of the free group on two generators.
- C, the complex numbers
- Function spaces C0((0, 1)) and C([0, 1]). Note that the first only has 0 as a projection. If K is a compact Hausdorff space, then C(K) is a projectionless algebra if and only if K is connected.
Last modified on 11 August 2012, at 10:05