[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2018.26.3.459

A NOTE ON NONLINEAR SKEW LIE TRIPLE DERIVATION BETWEEN PRIME ⁎-ALGEBRAS

Taghavi, Ali (Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran)
Nouri, Mojtaba (Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran)
Darvish, Vahid (Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran)

Publication Information

Korean Journal of Mathematics / v.26, no.3, 2018 , pp. 459-465 More about this Journal

Abstract

Recently, Li et al proved that ${\Phi}$ which satisfies the following condition on factor von Neumann algebras $$${\Phi}([[A,B$ $]$ $_*,C$ $]$ $_*)=[[{\Phi}(A),B$ $]$ $_*,C$ $]$ $_*+[[A,{\Phi}(B)$ $]$ $_*,C$ $]$ $_*+[[A,B$ $]$ $_*,{\Phi}(C)$ $]$ $_*$$$ where $$[A,B$ $]$ $_*=AB-BA^*$$ for all $A,B{\in}{\mathcal{A}}$ , is additive ${\ast}-derivation$ . In this short note we show the additivity of ${\Phi}$ which satisfies the above condition on prime ${\ast}-algebras$ .

Keywords

Lie triple derivation; prime ${\ast}-algebras$ ; additive map;

Citations & Related Records

Reference

1	Z. Bai and S. Du, The structure of non-linear Lie derivations on factor von Neumann algebras, Linear Algebra Appl. 436 (2012), 2701-2708. DOI
2	J. Cui and C.K. Li, Maps preserving product XY - Y X* on factor von Neumann algebras, Linear Algebra Appl. 431 (2009), 833-842. DOI
3	C. Li, F. Lu and X. Fang, Nonlinear $\xi$ -Jordan $\ast$ -derivations on von Neumann algebras, Linear and Multilinear Algebra. 62 (2014), 466-473. DOI
4	C. Li, F. Lu and X. Fang, Nonlinear mappings preserving product XY + Y X* on factor von Neumann algebras, Linear Algebra Appl. 438 (2013), 2339-2345. DOI
5	C. LI, F Zhao and Q. Chen, Nonlinear Skew Lie Triple Derivations between Factors, Acta Mathematica Sinica 32 (2016), 821-830. DOI
6	L. Molnar, A condition for a subspace of B(H) to be an ideal, Linear Algebra Appl. 235 (1996), 229-234. DOI
7	A. Taghavi, V. Darvish and H. Rohi, Additivity of maps preserving products AP ${\pm}$ PA* on C*-algebras, Mathematica Slovaca 67 (2017), 213-220.
8	A. Taghavi, H. Rohi and V. Darvish, Non-linear -Jordan derivations on von Neumann algebras, Linear Multilinear Algebra 64 (2016), 426-439. DOI
9	W. Yu and J. Zhang, Nonlinear $\ast$ -Lie derivations on factor von Neumann algebras, Linear Algebra Appl. 437 (2012), 1979-1991. DOI