$*$-Jordan-type maps on $C^{*}$-algebras

$*$-Lie-type maps on $C^*$-algebras

“…The next result can be found in [6] but for brevity we put the proof here Claim 2.2. Let X, Y and H be in…”

“…Furthermore, they generalize the Main Theorem in [5]. With this picture in mind, in this article we will discuss when a multiplicative * -Lie n-map is a * -isomorphism and, just as it was done in [6], we provide an application on von Neumann algebras, factor von Neumann algebras and prime algebras. Let us define the following sequence of polynomials, as presented in [7]:…”

“…In [7], 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 proved that, under certain conditions, an application between C * -algebras that is multiplicative * -Lie n-map and multiplicative * -Jordan n-map is a * -ring isomorphism. In the second paper of this series [6], Ferreira and Costa prove when a multiplicative * -Jordan n-map is a * -ring isomorphism. As a consequence of their main result, they provide an application on von Neumann algebras, factor von Neumann algebras and prime algebras.…”