Projectionless algebra

In mathematics, a projectionless C*-algebra is a C*-algebra in which 0 and 1 are the only projections.

Examples

• 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.