Commutation theorem for traces: Difference between revisions

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{{Short description|Identifies the commutant of a specific von Neumann algebra}}

In [[mathematics]], a '''commutation theorem for traces''' explicitly identifies the [[commutant]] of a specific [[von Neumann algebra]] acting on a [[Hilbert space]] in the presence of a [[Von Neumann algebra#Weights, states, and traces|trace]].

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==References==

*{{citation|firstfirst1=O.|lastlast1=Bratteli|first2=D.W.|last2=Robinson|title=Operator Algebras and Quantum Statistical Mechanics 1, Second Edition|publisher=Springer-Verlag|year=1987|isbn=3-540-17093-6}}

*{{citation|first=A.|last=Connes|authorlink=Alain Connes|title=Sur la théorie non commutative de l’intégrationl'intégration|series=Lecture Notes in Mathematics|volume=(Algèbres d'Opérateurs)|publisher=Springer-Verlag|year=1979|pages=19–143|isbn=978-3-540-09512-5}}

*{{citation|first=J.|last = Dieudonné|authorlink=Jean Dieudonné|title=Treatise on Analysis, Vol. II |year=1976|publisher=Academic Press|isbn=0-12-215502-5}}

*{{citation|first=J.|last= Dixmier|authorlink=Jacques Dixmier|title=Les algèbres d'opérateurs dans l'espace hilbertien: algèbres de von Neumann|publisher= Gauthier-Villars |year=1957}}

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*{{citation|first=R.|last=Godement|authorlink=Roger Godement|title=Mémoire sur la théorie des caractères dans les groupes localement compacts unimodulaires|journal=J. Math. Pures Appl.|volume= 30|year=1951|pages=1–110}}

*{{citation|first=R.|last=Godement|authorlink=Roger Godement|title=Théorie des caractères. I. Algèbres unitaires|journal=Ann. of Math.|volume= 59|year=1954|pages=47–62|doi=10.2307/1969832|issue=1|publisher=Annals of Mathematics|jstor=1969832}}

*{{citation|firstfirst1=F.J.|lastlast1= Murray|authorlink1=Francis Joseph Murray|first2= J. |last2=von Neumann |authorlink2=John von Neumann

|title=On rings of operators| journal= Ann. of Math. |series= 2 |volume= 37 |year=1936|pages=116–229|doi=10.2307/1968693|jstor=1968693|issue=1|publisher=Annals of Mathematics}}

*{{citation|firstfirst1=F.J.|lastlast1= Murray|authorlink1=Francis Joseph Murray|first2= J. |last2=von Neumann|authorlink2=John von Neumann

|title=On rings of operators II|journal= Trans. Amer. Math. Soc. |volume= 41 |year=1937|pages= 208–248|doi=10.2307/1989620|issue=2|jstor=1989620|publisher=American Mathematical Society|doi-access=free}}

*{{citation|firstfirst1=F.J.|lastlast1= Murray|authorlink1=Francis Joseph Murray|first2= J. |last2=von Neumann |authorlink2=John von Neumann

|title=On rings of operators IV|journal= Ann. of Math. |series= 2 |volume= 44 |year=1943|pages= 716–808|doi=10.2307/1969107|jstor=1969107|issue=4|publisher=Annals of Mathematics}}

*{{citation|last=Pedersen|first=G.K.|title=C* algebras and their automorphism groups|series=London Mathematical Society Monographs|volume=14|year=1979|

publisher=Academic Press|isbn=0-12-549450-5}}

*{{citation|lastlast1=Rieffel|firstfirst1= M.A.|last2= van Daele|first2=A.|title=A bounded operator approach to Tomita–Takesaki theory|journal=Pacific J. Math.|volume= 69 |year=1977|pages= 187–221|doi=10.2140/pjm.1977.69.187|doi-access=free}}

*{{citation|last=Segal|first=I.E.| authorlink=Irving Segal|title=A non-commutative extension of abstract integration|journal=Ann. of Math. |volume=57|year=1953|pages= 401–457|doi=10.2307/1969729|issue=3|publisher=Annals of Mathematics|jstor=1969729}} (Section 5)

*{{citation|last=Simon|first= B.|authorlink=Barry Simon|title=Trace ideals and their applications|series=London Mathematical Society Lecture Note Series|volume= 35|publisher= Cambridge University Press|year= 1979|isbn = 0-521-22286-9}}