Geodesic
Mappings preserving sum of products $a\circ b+ba^{*}$ on factor von Neumann algebras
Algebra and discrete mathematics, Tome 31 (2021) no. 1, pp. 61-70 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $\mathcal{A}$ and $\mathcal{B}$ be two factor von Neumann algebras. In this paper, we proved that a bijective mapping $\Phi \colon\mathcal{A}\to\mathcal{B}$ satisfies $\Phi (a\circ b+ba^{*})=\Phi (a)\circ \Phi (b)+\Phi (b)\Phi (a)^{*}$ (where $\circ $ is the special Jordan product on $\mathcal{A}$ and $\mathcal{B},$ respectively), for all elements $a,b\in \mathcal{A}$, if and only if $\Phi $ is a $\ast $-ring isomorphism. In particular, if the von Neumann algebras $\mathcal{A}$ and $\mathcal{B}$ are type I factors, then $\Phi $ is a unitary isomorphism or a conjugate unitary isomorphism.
Keywords: $\ast$-ring isomorphisms, factor von Neumann algebras. 
@article{ADM_2021_31_1_a3,
     author = {J. C. Ferreira and M. G. B. Marietto},
     title = {Mappings preserving sum of products $a\circ b+ba^{*}$ on factor von {Neumann} algebras},
     journal = {Algebra and discrete mathematics},
     pages = {61--70},
     year = {2021},
     volume = {31},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a3/}
}
TY  - JOUR
AU  - J. C. Ferreira
AU  - M. G. B. Marietto
TI  - Mappings preserving sum of products $a\circ b+ba^{*}$ on factor von Neumann algebras
JO  - Algebra and discrete mathematics
PY  - 2021
SP  - 61
EP  - 70
VL  - 31
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a3/
LA  - en
ID  - ADM_2021_31_1_a3
ER  - 
%0 Journal Article
%A J. C. Ferreira
%A M. G. B. Marietto
%T Mappings preserving sum of products $a\circ b+ba^{*}$ on factor von Neumann algebras
%J Algebra and discrete mathematics
%D 2021
%P 61-70
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a3/
%G en
%F ADM_2021_31_1_a3
J. C. Ferreira; M. G. B. Marietto. Mappings preserving sum of products $a\circ b+ba^{*}$ on factor von Neumann algebras. Algebra and discrete mathematics, Tome 31 (2021) no. 1, pp. 61-70. http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a3/

[1] P. Ji, Z. Liu, “Additivity of Jordan maps on standard Jordan operator algebras”, Linear Algebra Appl., 430 (2009), 335–343 | DOI | MR | Zbl

[2] C. Li, F. Lu, X. Fang, “Nonlinear mappings preserving product $XY+YX^{*}$ on factor von Neumann algebras”, Linear Algebra Appl., 438 (2013), 2339–2345 | DOI | MR | Zbl

[3] L. Liu, G. Ji, “Maps preserving product $X^{*}Y+YX^{*}$ on factor von Newmann algebras”, Linear Algebra Appl., 59 (2011), 951–955 | MR | Zbl

[4] F. Lu, “Additivity of Jordan maps on standard operator algebras”, Linear Algebra Appl., 357 (2002), 123–131 | DOI | MR | Zbl

[5] L. W. Marcoux, A. R. Sourour, “Lie isomorphisms of nest algebras”, J. Funct. Anal., 164 (1999), 163–180 | DOI | MR | Zbl

[6] J. Qian, P. Li, “Additivity of Lie maps on operator algebras”, Bull. Korean Math. Soc., 44 (2007), 271–279 | DOI | MR | Zbl

[7] M. Wang, G. Ji, “Maps preserving $\ast$-Lie product on factor von Neumann algebras”, Linear Multilinear Algebra, 64 (2016), 2159–2168 | DOI | MR | Zbl