Projectionless algebra

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.

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.

References

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