In the theory of von Neumann algebras, a part of the mathematical field of functional analysis, Tomita–Takesaki theory is a method for constructing modular automorphisms of von Neumann algebras from the polar decomposition of a certain involution. It is essential for the theory of type III factors, and has led to a good structure theory for these previously intractable objects. The theory was introduced by Minoru Tomita (), but his work was hard to follow and mostly unpublished, and little notice was taken of it until Masamichi Takesaki () wrote an account of Tomita's theory.

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dbo:abstract
  • Die Tomita-Takesaki-Theorie, benannt nach M. Tomita und M. Takesaki, auch als modulare Theorie bekannt, ist eine Theorie aus dem mathematischen Teilgebiet der Funktionalanalysis, genauer der Theorie der Von-Neumann-Algebren. Einer Von-Neumann-Algebra wird eine Gruppe von Automorphismen zugeordnet, mit der die Struktur der Von-Neumann-Algebra näher untersucht werden kann. (de)
  • In the theory of von Neumann algebras, a part of the mathematical field of functional analysis, Tomita–Takesaki theory is a method for constructing modular automorphisms of von Neumann algebras from the polar decomposition of a certain involution. It is essential for the theory of type III factors, and has led to a good structure theory for these previously intractable objects. The theory was introduced by Minoru Tomita (), but his work was hard to follow and mostly unpublished, and little notice was taken of it until Masamichi Takesaki () wrote an account of Tomita's theory. (en)
  • 함수해석학에서, 모듈러 자기 동형(modular自己同型, 영어: modular automorphism)은 힐베르트 공간의 한 단위 벡터로 정의되는, 폰 노이만 대수의 특별한 자기 동형이다. 이를 사용하여 인자 대수 및 폰 노이만 대수를 분류할 수 있다. (ko)
dbo:wikiPageExternalLink
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  • 2898625 (xsd:integer)
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  • 9899 (xsd:integer)
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  • 964681518 (xsd:integer)
dbo:wikiPageWikiLink
dbp:authorlink
  • Masamichi Takesaki (en)
  • Minoru Tomita (en)
dbp:bot
  • InternetArchiveBot (en)
dbp:date
  • January 2018 (en)
dbp:first
  • A. (en)
  • A.I. (en)
  • Minoru (en)
  • Masamichi (en)
dbp:fixAttempted
  • yes (en)
dbp:id
  • H/h047230 (en)
  • T/t120150 (en)
dbp:last
  • Tomita (en)
  • Inoue (en)
  • Shtern (en)
  • Takesaki (en)
dbp:title
  • Hilbert algebra (en)
  • Tomita–Takesaki theory (en)
dbp:wikiPageUsesTemplate
dbp:year
  • 1967 (xsd:integer)
  • 1970 (xsd:integer)
dct:subject
rdf:type
rdfs:comment
  • Die Tomita-Takesaki-Theorie, benannt nach M. Tomita und M. Takesaki, auch als modulare Theorie bekannt, ist eine Theorie aus dem mathematischen Teilgebiet der Funktionalanalysis, genauer der Theorie der Von-Neumann-Algebren. Einer Von-Neumann-Algebra wird eine Gruppe von Automorphismen zugeordnet, mit der die Struktur der Von-Neumann-Algebra näher untersucht werden kann. (de)
  • In the theory of von Neumann algebras, a part of the mathematical field of functional analysis, Tomita–Takesaki theory is a method for constructing modular automorphisms of von Neumann algebras from the polar decomposition of a certain involution. It is essential for the theory of type III factors, and has led to a good structure theory for these previously intractable objects. The theory was introduced by Minoru Tomita (), but his work was hard to follow and mostly unpublished, and little notice was taken of it until Masamichi Takesaki () wrote an account of Tomita's theory. (en)
  • 함수해석학에서, 모듈러 자기 동형(modular自己同型, 영어: modular automorphism)은 힐베르트 공간의 한 단위 벡터로 정의되는, 폰 노이만 대수의 특별한 자기 동형이다. 이를 사용하여 인자 대수 및 폰 노이만 대수를 분류할 수 있다. (ko)
rdfs:label
  • Tomita-Takesaki-Theorie (de)
  • Tomita–Takesaki theory (en)
  • 모듈러 자기 동형 (ko)
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