Abelian von Neumann algebra

In functional analysis, a branch of mathematics, an abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements commute. The prototypical example of an abelian von Neumann algebra is the algebra L∞(X, μ) for μ a σ-finite measure on X realized as an algebra of operators on the Hilbert space L2(X, μ) as follows: Each f ∈ L∞(X, μ) is identified with the multiplication operator ψ ↦ f ψ .

Source: Wikipedia — Abelian von Neumann algebra (CC BY-SA 4.0)

Abelian von Neumann algebra

In functional analysis, a branch of mathematics, an abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements commute. The prototypical example of an abelian von Neumann algebra is the algebra L∞(X, μ) for μ a σ-finite measure on X realized as an algebra of operators on the Hilbert space L2(X, μ) as follows: Each f ∈ L∞(X, μ) is identified with the multiplication operator ψ ↦ f ψ .

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Source: Wikipedia "Abelian von Neumann algebra" · CC BY-SA 4.0

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