A note on non-linear $*$-Jordan derivations on $*$-algebras

Rok, strany: 2019, 639 - 646

Taghavi et al. in [\uppercase{Taghavi, A.—Rohi, H.—Darvish, V.}: \textit{Non-linear $*$-Jordan derivations on von Neumann algebras}, Linear Multilinear Algebra \textbf{64} (2016), 426–439] proved that the map $Φ:\mathcal{A}\to\mathcal{A}$ which satisfies the following condition

$$Φ(A\diamond B)=Φ(A)\diamond B+A\diamond Φ(B)$$

where $A \diamond B=AB+BA^*$ for every $A,B\in\mathcal{A}$ is an additive $*$-derivation. In this short note, we prove that when A is a prime $*$-algebras and $Φ:\mathcal{A} \to \mathcal{A}$ satisfies the above condition, then $Φ$ is $*$-additive. Moreover, if $Φ(iI)$ is self-adjoint then $Φ$ is derivation.

ISO 690:

Taghavi, M., Nouri, M., Razeghi, M., Darvish, V. 2019. A note on non-linear $*$-Jordan derivations on $*$-algebras. In Mathematica Slovaca, vol. 69, no.3, pp. 639-646. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0253

APA:

Taghavi, M., Nouri, M., Razeghi, M., Darvish, V. (2019). A note on non-linear $*$-Jordan derivations on $*$-algebras. Mathematica Slovaca, 69(3), 639-646. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0253