von Neumann algebras of dimension greater than one contain non-trivial projections
- Let be a von Neumann algebra of dimension
greater than one acting on an Hilbert space
. Then contains a non-trivial projection, i.e. a projection that is not the zero (http://planetmath.org/ZeroMap) the identity operator.
- As in the theory of -algebras, for a projection we mean an orthogonal projection.