Editing Von Neumann algebra (section)

==References==

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*{{citation |first1=H. |last1=Araki |first2=E. J. |last2=Woods |title=A classification of factors |journal=Publ. Res. Inst. Math. Sci. Ser. A |volume=4 |year=1968 |issue=1 |pages=51–130 |doi=10.2977/prims/1195195263 |doi-access=free}}{{MathSciNet|id=0244773}}
*{{citation |first=B. |last=Blackadar |title=Operator algebras |isbn=3-540-28486-9 |publisher=Springer |year=2005}}, {{citation |url=http://wolfweb.unr.edu/homepage/bruceb/Cycr.pdf |title=corrected manuscript |year=2013}} 
*{{citation |doi=10.2307/1971057 |first=A. |last=Connes |title=Classification of Injective Factors |journal=Annals of Mathematics |series=Second Series |volume=104 |issue=1 |year=1976 |pages=73–115 |jstor=1971057}}
*{{citation |first=A. |last=Connes |url=https://archive.org/details/noncommutativege0000conn |title=Non-commutative geometry |isbn=0-12-185860-X |year=1994 |publisher=Academic Press |url-access=registration}}.
*{{citation |first=J.|last=Dixmier |title=Von Neumann algebras |isbn=0-444-86308-7 |year=1981|publisher=凡異出版社 }} (A translation of {{citation |first=J. |last=Dixmier |title=Les algèbres d'opérateurs dans l'espace hilbertien: algèbres de von Neumann |publisher=Gauthier-Villars |year=1957}}, the first book about von Neumann algebras.)
*{{citation |first=V.F.R. |last=Jones |year=2003 |url=http://www.math.berkeley.edu/~vfr/MATH20909/VonNeumann2009.pdf |title=von Neumann algebras}}; incomplete notes from a course.
*{{citation |first=R.P.|last=Kostecki |year=2013 |arxiv=1307.4818 |title=W*-algebras and noncommutative integration |bibcode=2013arXiv1307.4818P}}.
*{{citation |first=Dusa |last=McDuff |author-link=Dusa McDuff |title=Uncountably many II<sub>1</sub> factors |journal=Annals of Mathematics |series=Second Series |volume=90 |year=1969 |pages=372–377 |doi=10.2307/1970730 |jstor=1970730 |issue=2}}
*{{citation |last=Murray |first=F. J.|contribution=The rings of operators papers |title=The legacy of John von Neumann (Hempstead, NY, 1988) |pages=57–60 |series=Proc. Sympos. Pure Math. |year=2006 |volume=50 |publisher=Amer. Math. Soc. |isbn=0-8218-4219-6 |location=Providence, RI.}} A historical account of the discovery of von Neumann algebras.
*{{citation |first1=F.J. |last1=Murray |first2=J. |last2=von Neumann |title=On rings of operators |journal=Annals of Mathematics |series=Second Series |volume=37 |year=1936 |pages=116–229 |doi=10.2307/1968693 |jstor=1968693 |issue=1}}. This paper gives their basic properties and the division into types I, II, and III, and in particular finds factors not of type I.  
*{{citation |first1=F.J. |last1=Murray |first2=J. |last2=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}}. This is a continuation of the previous paper, that studies properties of the trace of a factor. 
*{{citation |first1=F.J.|last1=Murray |first2=J. |last2=von Neumann |title=On rings of operators IV |journal=Annals of Mathematics |series=Second Series |volume=44 |year=1943 |pages=716–808 |doi=10.2307/1969107 |jstor=1969107 |issue=4}}. This studies when factors are isomorphic, and in particular shows that all approximately finite factors of type II<sub>1</sub> are isomorphic. 
*{{citation |doi=10.2307/1970364 |title=Representations of Uniformly Hyperfinite Algebras and Their Associated von Neumann Rings |first=Robert T. |last=Powers |author1-link=Robert T. Powers |journal=Annals of Mathematics |series=Second Series |volume=86 |issue=1 |year=1967 |pages=138–171 |jstor=1970364}}
*{{citation |first=S. |last=Sakai |author-link=Shoichiro Sakai |title=C*-algebras and W*-algebras |publisher=Springer |year=1971 |isbn=3-540-63633-1}}
*{{citation |author-link=Jacob T. Schwartz |first=Jacob |last=Schwartz |title=W-* Algebras |year=1967 |publisher=Gordon & Breach Publishing |isbn=0-677-00670-5}}
*{{springer|id=V/v096900|title=von Neumann algebra|first=A.I.|last=Shtern}}
*{{citation |first=M. |last=Takesaki |title=Theory of Operator Algebras I, II, III |isbn=3-540-42248-X |year=1979|publisher=Springer }}
<!-- Please do NOT change von to Von: this breaks the citation links. -->
*{{citation |first=J. |last=von Neumann |doi=10.1007/BF01782352 |title=Zur Algebra der Funktionaloperationen und Theorie der normalen Operatoren |journal= Math. Ann. |volume=102 |issue=1 |year=1930 |pages=370–427 |bibcode=1930MatAn.102..685E |s2cid=121141866}}. The original paper on von Neumann algebras.
*{{citation |doi=10.2307/1968692 |first=J. |last=von Neumann |title=On a Certain Topology for Rings of Operators |journal=Annals of Mathematics |series=Second Series |volume=37 |issue=1 |year=1936 |pages=111–115 |jstor=1968692}}. This defines the ultrastrong topology.
*{{citation |first=J. |last=von Neumann |url=http://www.numdam.org/item?id=CM_1939__6__1_0 |title=On infinite direct products |journal=Compos. Math. |volume=6 |year=1938 |pages=1–77}}. This discusses infinite tensor products of Hilbert spaces and the algebras acting on them.
*{{citation |first=J. |last=von Neumann |title=On rings of operators III |journal=Annals of Mathematics |series=Second Series |volume=41 |year=1940 |pages=94–161 |doi=10.2307/1968823 |jstor=1968823 |issue=1}}. This shows the existence of factors of type III. 
*{{citation |doi=10.2307/1969106 |first=J. |last=von Neumann |title=On Some Algebraical Properties of Operator Rings |journal=Annals of Mathematics |series=Second Series |volume=44 |issue=4 |year=1943 |pages=709–715 |jstor=1969106}}. This shows that some apparently topological properties in von Neumann algebras can be defined purely algebraically. 
*{{citation |doi=10.2307/1969463 |first=J. |last=von Neumann |title=On Rings of Operators. Reduction Theory |journal=Annals of Mathematics |series=Second Series |volume=50 |issue=2 |year=1949 |pages=401–485 |jstor=1969463}}. This discusses how to write a von Neumann algebra as a sum or integral of factors.
*{{citation |last=von Neumann |first=John |title=Collected Works, Volume III: Rings of Operators |editor-first=A.H. |editor-last=Taub |location=NY |publisher=Pergamon Press |year=1961}}. Reprints von Neumann's papers on von Neumann algebras.
*{{citation |first=A. J. |last=Wassermann |author-link=Antony Wassermann |year=1991 |url=http://iml.univ-mrs.fr/~wasserm/OHS.ps |title=Operators on Hilbert space}}

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[[Category:Operator theory]]
[[Category:Von Neumann algebras|*]]
[[Category:John von Neumann]]