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

- Let $ℳ$ be a von Neumann algebra of dimension greater than one acting on an Hilbert space $H$. Then $ℳ$ 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
Canonical name	VonNeumannAlgebrasOfDimensionGreaterThanOneContainNontrivialProjections
Date of creation	2013-03-22 17:29:00
Last modified on	2013-03-22 17:29:00
Owner	asteroid (17536)
Last modified by	asteroid (17536)
Numerical id	5
Author	asteroid (17536)
Entry type	Result
Classification	msc 46L10