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Direct integral

In mathematics and functional analysis, a direct integral or Hilbert integral is a generalization of the concept of a direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was introduced in 1949 by John von Neumann in one of the papers in the series On Rings of Operators.…

Standards, Direct integrals of Hilbert spaces & Decomposable operators

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Direct integrals of Hilbert spaces

Decomposable operators

Central decomposition

Measurable families of representations

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Direct integral

Nodes45
Edges44
Triples12
Avg. degree1.96
Density0.044444
Components1

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Direct integral

Top relations

related to Decomposition of Abelian von Neumann algebras · 7
Direct integral → Abelian, Borel, For, Hilbert, Neumann, The, Theorem
related to Direct integrals of Hilbert spaces · 5
Direct integral → H-valued, Hilbert, L2, Somewhat, The

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Important terminology

von neumann measurable operators hilbert direct spaces algebra algebras space theorem separable measure integral family one borel theory decomposition representations

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Direct integralrelated to Decomposition of Abelian von Neumann algebrasThe0.60section
Direct integralrelated to Decomposition of Abelian von Neumann algebrasTheorem0.60section
Direct integralrelated to Decomposition of Abelian von Neumann algebrasFor0.60section
Direct integralrelated to Decomposition of Abelian von Neumann algebrasAbelian0.60section
Direct integralrelated to Decomposition of Abelian von Neumann algebrasNeumann0.60section
Direct integralrelated to Decomposition of Abelian von Neumann algebrasHilbert0.60section
Direct integralrelated to Decomposition of Abelian von Neumann algebrasBorel0.60section
Direct integralrelated to Direct integrals of Hilbert spacesThe0.60section
Direct integralrelated to Direct integrals of Hilbert spacesL20.60section
Direct integralrelated to Direct integrals of Hilbert spacesSomewhat0.60section
Direct integralrelated to Direct integrals of Hilbert spacesHilbert0.60section
Direct integralrelated to Direct integrals of Hilbert spacesH-valued0.60section

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