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

2014/04/30 by Burgos, María, Fernández-Polo, Francisco J., Garcés, Jorge J. +1
#15A99 #16S50 #46L40 #46L57 #47A #47B47 #47B49 #47D25 #47L30 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1404.7597

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.

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