Commutativity preserving mappings of von Neumann algebras

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dc.contributor.authorBresar, Matej
dc.contributor.authorMiers, C. Robert
dc.date.accessioned2010-01-07T00:25:11Z
dc.date.available2010-01-07T00:25:11Z
dc.date.copyright1991en
dc.date.issued2010-01-07T00:25:11Z
dc.description.abstractA map \theta: M->N where M and N are rings is said to preserve commutativity in both directions if the elements a,b \in M commute if and only if \theta(a) and \theta(b) commute. In this paper we show that if M and N are von Neumann algebras with no central summands of type I_1 or I_2 and \theta is a bijective map which preserves commutativity in both directions then \theta(x)=c\phi(x)+f(x) where c is an invertible element in Z_N, the center of N, \phi:M->N is a Jordan isomorphism of M onto N, and f is an additive map of M into Z_N.en
dc.identifier.urihttp://hdl.handle.net/1828/2036
dc.language.isoenen
dc.relation.ispartofseriesDMS-589-IRen
dc.subjecttechnical reports (mathematics and statistics)
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleCommutativity preserving mappings of von Neumann algebrasen
dc.typeTechnical Reporten

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