Abelian von Neumann algebra
id:
abelian-von-neumann-algebra-245-13536135
title:
Abelian von Neumann algebra
text:
In functional analysis, 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 Of particular importance are the abelian von Neumann algebras on separable Hilbert spaces, particular
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https://en.wikipedia.org/wiki/Abelian_von_Neumann_algebra
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date modified:
2024-02-16T15:36:12Z
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