$$*$$-Lie–Jordan-Type Maps on $$C^*$$-Algebras

Nonlinear *-Jordan-type derivations on alternative *-algebras

“…In [3], the authors proved that a map ϕ between two factor von Newmann algebras is a * -ring isomorphism if and only if ϕ({a, b} * ) = {ϕ(a), ϕ(b)} * . In [4], Ferreira and Costa extended these new products and defined two other types of applications, named multiplicative * -Lie n-map and multiplicative * -Jordan n-map and used them to impose condition such that a map between C * -algebras is a * -ring isomorphism. Even more, in [16], Taghavi et al considered the product a • b = a * b + ba * and studied when a bijective map is additive in * -algebras.…”

“…Throughout the paper, the ground field is assumed to be of complex numbers. Consider the product {x, y} * = xy + yx * and let us define the following sequence of polynomials, as defined in [4]: q 1 * (x) = x and q n * (x 1 , x 2 , . .…”

“…is the product introduced by Brešar and Fošner [1,12]. Then, using the nomenclature introduced in [4] we have a new class of maps (not necessarily additive):…”