Martin Mathieu, Queen's University Belfast (Koautor: Gerhard Schick)
In his 1982 proof of Johnson's uniqueness-of-the-complete-norm- topology theorem, Aupetit made essential use of the concept of 'spectral boundedness' of a (Jordan) epimorphism onto a semisimple Banach algebra. In a joint paper with my research student Gerhard Schick, we show that this property (essentially) characterises Jordan homomorphisms which are defined on properly infinite von Neumann algebras. This extends Aupetit's 2000 article on spectrum-preserving mappings (J. London Math. Soc. 2000) in this setting. We also discuss the obstruction that occurs in the case of finite von Neumann algebras.