Geodesic
Nonlinear maps preserving the mixed product [a • b, c] * on von Neumann algebras
Filomat, Tome 35 (2021) no. 8, p. 2775

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

Let A and B be two von Neumann algebras. For A, B ∈ A, define by [A, B] * = AB − BA * and A • B = AB + BA * the new products of A and B. Suppose that a bijective map Φ : A → B satisfies Φ([A • B, C] *) = [Φ(A) • Φ(B), Φ(C)] * for all A, B, C ∈ A. In this paper, it is proved that if A and B be two von Neumann algebras with no central abelian projections, then the map Φ(I)Φ is a sum of a linear *-isomorphism and a conjugate linear *-isomorphism, where Φ(I) is a self-adjoint central element in B with Φ(I) 2 = I. If A and B are two factor von Neumann algebras, then Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism
DOI : 10.2298/FIL2108775L
Classification : 47B48, 46L10
Keywords: Jordan ∗-product, isomorphism, von Neumann algebras 
Changjing Li; Yuanyuan Zhao; Fangfang Zhao. Nonlinear maps preserving the mixed product [a • b, c] * on von Neumann algebras. Filomat, Tome 35 (2021) no. 8, p. 2775 . doi: 10.2298/FIL2108775L
@article{10_2298_FIL2108775L,
     author = {Changjing Li and Yuanyuan Zhao and Fangfang Zhao},
     title = {Nonlinear maps preserving the mixed product [a {\textbullet} b, c] * on von {Neumann} algebras},
     journal = {Filomat},
     pages = {2775 },
     year = {2021},
     volume = {35},
     number = {8},
     doi = {10.2298/FIL2108775L},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2108775L/}
}
TY  - JOUR
AU  - Changjing Li
AU  - Yuanyuan Zhao
AU  - Fangfang Zhao
TI  - Nonlinear maps preserving the mixed product [a • b, c] * on von Neumann algebras
JO  - Filomat
PY  - 2021
SP  - 2775 
VL  - 35
IS  - 8
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2108775L/
DO  - 10.2298/FIL2108775L
LA  - en
ID  - 10_2298_FIL2108775L
ER  - 
%0 Journal Article
%A Changjing Li
%A Yuanyuan Zhao
%A Fangfang Zhao
%T Nonlinear maps preserving the mixed product [a • b, c] * on von Neumann algebras
%J Filomat
%D 2021
%P 2775 
%V 35
%N 8
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2108775L/
%R 10.2298/FIL2108775L
%G en
%F 10_2298_FIL2108775L

Cité par Sources :