# von Neumann algebras of dimension greater than one contain non-trivial projections

- Let $\mathcal{M}$ be a von Neumann algebra of dimension greater than one acting on an Hilbert space $H$. Then $\mathcal{M}$ contains a non-trivial projection, i.e. a projection that is not the zero (http://planetmath.org/ZeroMap) the identity operator.

$Note$ - As in the theory of $C^{*}$-algebras, for a projection we mean an orthogonal projection.

Title von Neumann algebras of dimension greater than one contain non-trivial projections VonNeumannAlgebrasOfDimensionGreaterThanOneContainNontrivialProjections 2013-03-22 17:29:00 2013-03-22 17:29:00 asteroid (17536) asteroid (17536) 5 asteroid (17536) Result msc 46L10