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arXiv · 1405.3836

2-local triple homomorphisms on von Neumann algebras and JBW$^*$-triples

Maria Burgos·Francisco J. FernÁndez-Polo·Jorge J. GarcÉs·Antonio M. Peralta
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Abstract

We prove that every (not necessarily linear nor continuous) 2-local triple homomorphism from a JBW$^*$-triple into a JB$^*$-triple is linear and a triple homomorphism. Consequently, every 2-local triple homomorphism from a von Neumann algebra (respectively, from a JBW$^*$-algebra) into a C$^*$-algebra (respectively, into a JB$^*$-algebra) is linear and a triple homomorphism.

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Maria Burgos, Francisco J. FernÁndez-Polo, Jorge J. GarcÉs, Antonio M. Peralta. 2014-05-15. 2-local triple homomorphisms on von Neumann algebras and JBW$^*$-triples. https://arxiv.org/abs/1405.3836

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