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


- Let be a von Neumann algebraMathworldPlanetmathPlanetmathPlanetmath of dimensionPlanetmathPlanetmath greater than one acting on an Hilbert spaceMathworldPlanetmath H. Then 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*-algebrasPlanetmathPlanetmath, 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