About: Tomita–Takesaki theory

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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 The theory was introduced by Minoru Tomita, but his work was hard to follow and mostly unpublished, and little notice was taken of it until Masamichi Takesaki wrote an account of Tomita's theory.

Attributes	Values
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rdfs:label	Tomita-Takesaki-Theorie (de) 모듈러 자기 동형 (ko) Tomita–Takesaki theory (en)
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 The theory was introduced by Minoru Tomita, but his work was hard to follow and mostly unpublished, and little notice was taken of it until Masamichi Takesaki wrote an account of Tomita's theory.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:seeAlso	Commutation theorem for traces
dcterms:subject	Operator theory Von Neumann algebras
Wikipage page ID	2898625 (xsd:integer)
Wikipage revision ID	1119698047 (xsd:integer)
Link from a Wikipage to another Wikipage	Cyclic and separating vector Von Neumann algebra Operator theory Gelfand–Naimark–Segal construction Quantum statistical mechanics Commutation theorem for traces Functional analysis Springer Publishing Alain Connes Outer automorphism group Journal of Mathematical Physics KMS state Hilbert space Von Neumann algebras Academic Press Polar decomposition Spectral theorem Springer-Verlag Commutant
Link from a Wikipage to an external page	https://archive.org/details/noncommutativege0000conn https://link.springer.com/book/10.1007/978-1-4613-8669-8%7Ctitle=An http://www.numdam.org/article/ASENS_1973_4_6_2_133_0.pdf%7Clast=Connes http://www.lqp.uni-goettingen.de/papers/99/04/99042900.html https://projecteuclid.org/journals/pacific-journal-of-mathematics/volume-75/issue-1/A-simple-proof-of-the-existence-of-modular-automorphisms-in/pjm/1102810157.full
sameAs	Tomita–Takesaki theory Tomita–Takesaki theory Tomita–Takesaki theory Tomita–Takesaki theory Tomita–Takesaki theory
dbp:wikiPageUsesTemplate	dbt:Banach_spaces dbt:= dbt:Citation dbt:Dead_link dbt:Harvtxt dbt:Reflist dbt:See_also dbt:Sfn dbt:Spectral_theory dbt:Harvs dbt:Eom dbt:Functional_analysis dbt:Rudin_Walter_Functional_Analysis dbt:Hilbert_space dbt:Text
authorlink	Masamichi Takesaki (en) Minoru Tomita (en)
bot	InternetArchiveBot (en)
date	January 2018 (en)
first	A. (en) A.I. (en) Minoru (en) Masamichi (en)
fix-attempted	yes (en)
id	H/h047230 (en) T/t120150 (en)
last	Tomita (en) Inoue (en) Shtern (en) Takesaki (en)
title	Hilbert algebra (en) Tomita–Takesaki theory (en)
year	1967 (xsd:integer) 1970 (xsd:integer)
has 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)
gold:hypernym	Method
prov:wasDerivedFrom	wikipedia-en:Tomita–Takesaki_theory?oldid=1119698047&ns=0
page length (characters) of wiki page	15100 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Tomita–Takesaki_theory
is rdfs:seeAlso of	Commutation theorem for traces
is Link from a Wikipage to another Wikipage of	Rudolf Haag Detlev Buchholz Cyclic and separating vector Uffe Haagerup Von Neumann algebra

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