Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras

Li, Changjing; Chen, Quanyuan; Wang, Ting

doi:10.1007/s11401-018-0086-4

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By the Injectivity Of φ We Concur That [([A B]1

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2020

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Cited by 22 publications

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“…Then A = B 2 for some self-adjoint element B ∈ A. It follows from Lemma 2.11 that φ(A) = φ(B) 2 . By Lemma 2.2, we get that φ(B) is self-adjoint.…”

Section: By the Injectivity Of φ We Concur That [([A B]mentioning

confidence: 96%

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

Zhang¹

2020

Preprint

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Let A and B be two factor von Neumann algebras and η be a non-zero complex number. A nonlinear bijective map φ : A → B has been demonstrated to satisfyfor all A, B, C ∈ 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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“…Then A = B 2 for some self-adjoint element B ∈ A. It follows from Lemma 2.11 that φ(A) = φ(B) 2 . By Lemma 2.2, we get that φ(B) is self-adjoint.…”

Section: By the Injectivity Of φ We Concur That [([A B]mentioning

confidence: 96%