Commutativity Preserving Mappings of Von Neumann Algebras

Brešar, Matej ; Miers, C. Robert

Canadian journal of mathematics, Tome 45 (1993) no. 4, pp. 695-708

Résumé

A map θ: M —> N where M and N are rings is said to preserve commutativity in both directions if the elements a,b ∊ M commute if and only if θ(a) and θ(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 θ is a bijective additive map which preserves commutativity in both directions then θ(x) = cφ(x) +f(x) where c is an invertible element in ZN , the center of N, φ M —> N is a Jordan isomorphism of M onto N, and f is an additive map of M into ZN .

Détail

DOI : 10.4153/CJM-1993-039-x

Mots-clés : 46L10, 16W10

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