A Kowalski-Słodkowski theorem for 2-local $^*$-homomorphisms on von Neumann algebras

Published 30 Apr 2014 in math.OA, math.FA, and math.SP | (1404.7597v1)

Abstract: It is established that every (not necessarily linear) 2-local $^{*$-homomorphism} from a von Neumann algebra into a C$^*$-algebra is linear and a $^{*$-homomorphism.} In the setting of (not necessarily linear) 2-local $^{*$-homomorphism} from a compact C$^*$-algebra we prove that the same conclusion remains valid. We also prove that every 2-local Jordan $^{*$-homomorphism} from a JBW$^*$-algebra into a JB$^*$-algebra is linear and a Jordan $^{*$-homomorphism.}