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- Direct_integral abstract "In mathematics and functional analysis a direct integral is a generalization of the concept of 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. One of von Neumann's goals in this paper was to reduce the classification of (what are now called) von Neumann algebras on separable Hilbert spaces to the classification of so-called factors. Factors are analogous to full matrix algebras over a field, and von Neumann wanted to prove a continuous analogue of the Artin–Wedderburn theorem classifying semi-simple rings.Results on direct integrals can be viewed as generalizations of results about finite-dimensional C*-algebras of matrices; in this case the results are easy to prove directly. The infinite-dimensional case is complicated by measure-theoretic technicalities. Direct integral theory was also used by George Mackey in his analysis of systems of imprimitivity and his general theory of induced representations of locally compact separable groups.".
- Direct_integral wikiPageExternalLink sici?sici=0003-486X%28194904%292%3A50%3A2%3C401%3AOROORT%3E2.0.CO%3B2-H.
- Direct_integral wikiPageID "1256105".
- Direct_integral wikiPageRevisionID "599451945".
- Direct_integral hasPhotoCollection Direct_integral.
- Direct_integral subject Category:Functional_analysis.
- Direct_integral subject Category:Measure_theory.
- Direct_integral subject Category:Von_Neumann_algebras.
- Direct_integral type Abstraction100002137.
- Direct_integral type Algebra106012726.
- Direct_integral type Cognition100023271.
- Direct_integral type Content105809192.
- Direct_integral type Discipline105996646.
- Direct_integral type KnowledgeDomain105999266.
- Direct_integral type Mathematics106000644.
- Direct_integral type PsychologicalFeature100023100.
- Direct_integral type PureMathematics106003682.
- Direct_integral type Science105999797.
- Direct_integral type VonNeumannAlgebras.
- Direct_integral comment "In mathematics and functional analysis a direct integral is a generalization of the concept of 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.".
- Direct_integral label "Direct integral".
- Direct_integral sameAs m.04mn57.
- Direct_integral sameAs Q5280347.
- Direct_integral sameAs Q5280347.
- Direct_integral sameAs Direct_integral.
- Direct_integral wasDerivedFrom Direct_integral?oldid=599451945.
- Direct_integral isPrimaryTopicOf Direct_integral.