A Kowalski-S{\l}odkowski theorem for 2-local $^*$-homomorphisms on von   Neumann algebras
  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. 
Mar\'ia Burgos, Francisco J. Fern\'andez-Polo, Jorge J. Garc\'es, and   Antonio M. Peralta
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