Nonlinear maps preserving the mixed Jordan triple η-*-product between factors

2020/07/07 by Zhang, Fangjuan
#47B48 #FOS: Mathematics #G.1.3 #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2007.03247

Abstract

Let A and B be two factor von Neumann algebras and η be a non-zero complex number. A nonlinear bijective map ϕ:\mathcal A→\mathcal B has been demonstrated to satisfy ϕ([A,B]_*^η\diamond_η C)=[ϕ(A),ϕ(B)]_*^η\diamond_ηϕ(C) for all A,B,C∈\mathcal A. If η=1, then ϕ is a linear *-isomorphism, a conjugate linear *-isomorphism, the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism. If η≠ 1 and satisfies ϕ(I)=1, then ϕ is either a linear *-isomorphism or a conjugate linear *-isomorphism.

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• Nonlinear maps preserving Jordan η-∗-n-products
• Nonlinear maps preserving sums of triple products on ∗ -algebras
• Nonlinear mixed Jordan triple *-derivations on factors
• Nonlinear mixed Jordan triple *-derivations on *-algebras
• Non-linear ∗-Jordan derivations on von Neumann algebras