Commutativity preserving mappings of von Neumann algebras
Date
2010-01-07T00:25:11Z
Authors
Bresar, Matej
Miers, C. Robert
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Abstract
A 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.
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technical reports (mathematics and statistics)