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单词 VonNeumannAlgebrasOfDimensionGreaterThanOneContainNontrivialProjections
释义

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.

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更新时间:2025/5/5 0:08:16