A Kowalski-Słodkowski theorem for 2-local *-homomorphisms on von Neumann algebras
Burgos, María · Fernández-Polo, Francisco J. · Garcés, Jorge J. · Peralta, Antonio M.
Operator Algebras
Functional Analysis
Spectral Theory
47B49, 46L40, 46L57, 47B47, 47D25, 47A, 15A99, 16S50, 47L30
Original · EN
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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