A projection in a C*-algebra is a self-adjoint idempotent,
that is, an element 
satisfying
 |
In an algebra of operators on a Hilbert space, it is the orthogonal projection onto a closed subspace
(Higson and Roe 2000). For example, 
is a projection in 
. Projections in matrix algebras
provide the classes defining topological K-theory.
The Kadison-Kaplansky conjecture
concerns projections in the reduced group C*-algebra
itself.
