# 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 |
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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 |