Jordan *-derivation pairs and quadratic functionals on modules over *-rings
The author offers a new proof and extension of a representation theorem by \textit{P. Šemrl} [Proc. Am. Math. Soc. 119, No. 4, 1105-1113 (1993; Zbl 0803.15024), cf. also ibid. 120, No. 2, 515-518 (1994; Zbl 0816.47040)] with aid of Jordan *-derivation pairs, which are defined as follows. Let \(K\) be a ring with involution *. The pair \(E, F\) of additive mappings of \(K\) into itself is a Jordan *-derivation pair if they satisfy the functional equation \(E(xyx)=E(x)y^*x^*+xF(y)x^*+xyE(x)\) for all \(x,y\in K\) and the similar equation with \(E\) and \(F\) interchanged.
scientific article; zbMATH DE number 1053597
scientific article